Advancing Sustainable Building Practices: Intelligent Methods for Enhancing Heating and Cooling Energy Efficiency

Abstract

Our work is dedicated to enhancing sustainability through improved energy efficiency in buildings, with a specific focus on heating and cooling control and the optimization of thermal comfort of occupants. With an energy consumption of more than 60% in buildings, HVAC systems are the biggest energy users. By integrating advanced technology, data algorithms, and digital twins, our study aims to optimize energy performance effectively. We have developed a Neural Network-based Model Predictive Control (NNMPC) to achieve this goal. Leveraging technologies such as MQTT communication, Wi-Fi modules, and field-programmable gate arrays will enhance scalability and flexibility. Our findings demonstrate the efficacy of the NNMPC system deployed on the PYNQ board for reducing sensible thermal energy usage for both cooling and heating purposes. Compared to traditional On/Off control systems, the NNMPC achieved an impressive 40.8% reduction in heating energy consumption and a 37.8% decrease in cooling energy consumption in 2006. In comparison to the On/Off technique, the NNMPC demonstrated a 25.6% reduction in annual heating energy consumption and a 28.8% drop in annual cooling energy consumption in the simulated year of 2017. We observed that, across all strategies and platforms, there were no instances where the Predicted Mean Vote (PMV) fell below $-0.5$. However, a significant proportion of PMV values (ranging from 65% to 83%) were observed between $-0.5$ and 0.5, signifying a high level of occupant comfort. Additionally, for PMV values between 0.5 and 1.0, percentages ranged from 16% to 33% for both years. Importantly, the NNMPC exhibited notable efficiency in maintaining occupants’ comfort within this range, requiring less energy while ensuring highly satisfactory environments.

1. Introduction

Efficient management of energy resources in the built environment is crucial for addressing contemporary challenges related to energy sustainability and environmental impact. The building sector, accounting for a substantial portion of global energy consumption [1], presents a significant opportunity for implementing strategies to enhance energy efficiency and reduce carbon emissions. For instance, in Morocco, it reached as high as 33% [2]. Improving a building’s energy efficiency involves a number of approaches, such as insulation, upgraded window glazing, and economizer controls, which can significantly reduce energy consumption [3,4,5,6,7,8,9]. Geographical location significantly influences the energy demands of HVAC systems, underlining the importance of global considerations in building design [9], and HVAC systems alone may account for more than 60% of a building’s energy use [10]. Control interventions demonstrate the potential for up to 34% energy savings, emphasizing the importance of optimized operation strategies [11].

Renewable energy integration should be prioritized alongside efficiency improvements, with a detailed understanding of a building’s energy requirements being crucial for optimal resource management. Simplified building energy models are highly desirable for evaluating and diagnosing building systems effectively [12]. Studies emphasize the need for holistic considerations in building design and energy management to achieve efficiency and cost-effectiveness [8].

In the quest for energy sustainability, the effectiveness of building energy models emerges as a fundamental element, providing information on energy use patterns and facilitating informed decision-making. However, while white-box models offer valuable information, they often fail to capture the subtleties of actual building dynamics and occupant behavior, leaving a notable gap in decision-making when controlling and optimizing HVAC systems. Traditional approaches like PID controllers face inefficiencies and overshoot issues, particularly in buildings with slow thermal dynamics. This highlights the necessity for adaptive, data-driven strategies that leverage advancements in ML and MPC to optimize energy usage while ensuring occupant comfort. Furthermore, the integration of material solutions into energy management practices remains a relatively unexplored avenue in the current literature. As a result, the need for sophisticated modeling techniques, combined with advanced control methods such as MPC, which reconciles technical precision with real-world complexities, is becoming increasingly apparent.

In summary, this introduction positions our study within the broader discourse of energy sustainability, addressing critical gaps in building energy modeling, control methodologies, and hardware implementations. By delving into these aspects, our research aims not only to reduce the demand for heating and cooling, which collectively constitute the majority of energy consumption in the building sector, but also to monitor and manage the thermal comfort of occupants. This focus on ensuring occupant comfort, coupled with the robustness of our proposed solution, distinguishes our work from a previous study [13] that concentrated on the feasibility of the proposed solution to reduce the energy furnished by HVAC systems. Finally, we want to catalyze the practical advances that will foster a future in which buildings guarantee both energy efficiency and the well-being of their occupants.

The structure of the remainder of this paper is arranged as follows. In Section 2, we delve into the current state of the art regarding modeling techniques for buildings and control strategies for optimizing thermal comfort within building environments. In Section 3, we present a concise introduction to the methodologies used to create the energy-building model. This section covers the creation of the NNMPC technique, the implementation process of the control law on the PYNQ board, and the data transfer between EnergyPlus and the PYNQ platform, where the NNMPC is applied. Section 4 presents the outcomes of our research. Section 5 presents a comparative analysis with findings from other studies focusing on energy reduction in buildings. To wrap up our discussion, in Section 6, we offer our concluding remarks and findings.

2. Background

2.1. Building Energy Modeling

As depicted in Figure 1, there are several approaches to building systems modeling, including the white-box, black-box, and gray-box methodologies. White-box modeling involves creating a system model based on a thorough understanding of the physical rules that define it [14]. In the context of building energy, white-box models simulate thermal behavior using resistance and capacitance networks to represent the building’s thermal properties [12,15,16,17]. White-box models consider factors like weather profiles, building architecture, occupant behavior, and control strategies [18].

In contrast, black-box modeling simplifies the system representation by ignoring its inner workings. This is usually applied in cases when the internal mechanisms are unreachable or too complex to be accurately depicted as a white-box model. Furthermore, they offer simplicity, rapid calculation, and benefits for analyzing building energy behavior and optimizing control strategies [19] but require substantial training data [20].

Gray-box models strike a compromise between the previous approaches. They employ fundamental physical equations with some level of simplicity. Similar to black-box models, gray-box models utilize recorded data for calibration to compensate for this simplicity. This makes it possible for the gray-box model to strike a balance between speed and precision. Gray-box models have been utilized across diverse components of building energy systems, effectively forecasting cooling capacity, electrical power input, and energy consumption using a variety of inputs [21,22]. Hybrid approaches that combine physical and ML techniques, as well as leveraging algorithms such as genetic algorithms (GA), have also been introduced [12,17].

Machine learning, commonly associated with black-box modeling, includes ANNs. The latter are designed to resemble brain networks seen in biology and have been used for modeling and predicting building temperatures [23]. In some studies, ANN and ML models have demonstrated accurate predictions and significant energy savings, especially in predicting building energy consumption [24]. Physical models are more relevant in the design of new buildings, while ML methods offer versatility for both new and existing buildings [14].

In order to reduce energy consumption and mitigate discomfort caused by HVAC systems, the utilization of reinforcement learning, particularly model-free Q-learning, has been suggested for optimal control decisions. This method assesses both internal and external environments dynamically and responds by choosing the optimal course of action in order to accomplish short- and long-term objectives [25]. Comparative case studies proved that rule-based heuristic control techniques were not as effective as reinforcement learning. In another study by Ref. [23], the influence of solar radiation, the water heating system, and the thermal behavior of a building were all modeled using ANNs. The study aimed to explore the possibility of employing ANNs to forecast interior temperature and enable proactive heating system controller deactivation for energy conservation.

In a broader overview, ANNs have found widespread application in the building sector for various energy-related tasks, showcasing their potential to enhance energy efficiency, reduce consumption, and improve overall system performance [24].

2.2. Control Methods for Buildings

Control methods for building heating and cooling systems have been extensively studied, and conventional PID controllers face inefficiency and overshoot issues in energy-efficient buildings with slow thermal dynamics [24]. Researchers have looked at data-driven techniques like deep reinforcement learning, model-based techniques like MPC, and optimum control to address the drawbacks of traditional controllers like PID [26,27,28,29,30]. MPC originated in the late 1970s [31,32], integrates a dynamic plant model within the control algorithm, that enables the controller to minimize a cost function and predict the future behavior of the plant. The iterative process involves forecasting future state variables, implementing optimal control, and continuously updating based on measured data.

MPC has become a widely adopted advanced control technology in various fields, including building automation and control [33]. For example, Ref. [15] proposed an MPC strategy for simultaneous temperature and humidity control in HVAC systems. The study by Ref. [34] compared predictive control schemes, including an ANN-based approach, emphasizing the importance of training data. Ref. [35] integrated MPC with ML for smart building control, improving prediction accuracy. Furthermore, two MPC algorithms, including a chance-constrained MPC, were created by Ref. [36] to dynamically balance energy usage and thermal comfort. The emphasis of Ref. [37] was on MPC and parameter identification for optimizing energy usage in HVAC systems. The study by Ref. [38] introduced an optimal controller using predictive control and the Lagrangian dual method. Moreover, Ref. [39] demonstrated the superiority of a learning-based MPC approach over conventional MPC for smart building thermal management. The simulation framework introduced by Ref. [40] used data-driven techniques for HVAC behavior emulation, leading to more significant energy savings. Our previous work [13] aimed to explore the feasibility of leveraging ANNs to forecast zone temperatures and facilitate proactive control of HVAC system controllers. This pioneering approach sought to conserve energy by integrating ANNs as an internal model within the MPC framework. The following section represents how to implement the proposed solution in more detail.

In summary, control strategies such as MPC, along with ML and data-driven approaches, are essential for maximizing energy efficiency and guaranteeing thermal comfort in building systems. These methods offer flexibility, adaptability, and significant energy-saving potential across various building applications.

3. Methodology

3.1. ANN Model

An ANN is a network of interconnected nodes, taking inspiration from a simplified model of neurons in the brain. In this context, each circular node symbolizes an artificial neuron, while an arrow signifies a connection, representing the flow of information from the output of one artificial neuron to the input of another (Figure 2). The structure of an artificial neuron, or formal neuron, entails calculating the weighted sum of its inputs x with weights W and adding a bias b. Afterward, this sum is passed through an activation function $f(.)$ to produce its output. For example, for the hidden layer, we can mathematically represent each neuron $a_i$ with $i\in [1,k]$, as in Equation (1), and for the output layer, each neuron $y_i$ with $i\in [1,m]$ can be represented as in Equation (2).

$$\begin{array}{c}\hfill \begin{array}{c}\hfill a_i=f(\sum _{j=1}^n{W}_{ij}·x_j+b_i)\end{array}\end{array}$$

(1)

$$\begin{array}{c}\hfill \begin{array}{c}\hfill y_i=f(\sum _{j=1}^k{W}_{ij}·a_j+b_i)\end{array}\end{array}$$

(2)

The primary goal in training the ANN is to identify a set of parameters within the ANN model that reduces the dissimilarity between the simulated and predicted data. The mathematical representation of an ANN can also be expressed in matrix form, Equations (3)–(5), especially for feed-forward neural networks. The architecture involves several key components. The weight matrix, denoted as $W^h$, connects the input layer to the hidden layer, possessing dimensions $k\times n$. Another weight matrix, $W^o$, with dimensions $m\times k$, links the hidden layer to the output layer. Additionally, there are two bias vectors, $B^h$ and $B^o$, with $k\times 1$ and $m\times 1$ elements, respectively. The vector $\mathbf{X}=[y\left(k\right),u^T\left(k\right),p^T\left(k\right)]$ consolidates the state variable, control variables, and perturbations, forming a $1\times n$ array. The activation function $f(.)$ relates to the hidden layer and applies a sigmoid-type function, specifically tansig, as outlined in Equation (6), element-wise to the matrix resultant from ${\mathbf{W}}^h·\mathbf{X}+{\mathbf{B}}^h$:

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill & \mathbf{Y}={\mathbf{W}}^o·f\left({\mathbf{W}}^h·\mathbf{X}+{\mathbf{B}}^h\right)+{\mathbf{B}}^o,\hfill \end{array}\end{array}$$

(3)

with

$${\mathbf{W}}^h=\left(\begin{array}{cccc}{W}_{1,1}& W_{1,2}& \cdots & W_{1,n}\\ W_{2,1}& W_{2,2}& \cdots & W_{2,n}\\ ⋮& ⋮& \ddots & ⋮\\ W_{k,1}& W_{k,2}& \cdots & W_{k,n}\end{array}\right),{\mathbf{B}}^h=\left(\begin{array}{c}{b}_1\\ b_2\\ ⋮\\ b_k\end{array}\right)$$

(4)

$${\mathbf{W}}^o=\left(\begin{array}{cccc}{W}_{1,1}& W_{1,2}& \cdots & W_{1,k}\\ W_{2,1}& W_{2,2}& \cdots & W_{2,k}\\ ⋮& ⋮& \ddots & ⋮\\ W_{m,1}& W_{m,2}& \cdots & W_{m,k}\end{array}\right),{\mathbf{B}}^o=\left(\begin{array}{c}{b}_1\\ b_2\\ ⋮\\ b_m\end{array}\right).$$

(5)

During the training process of the ANN, the Levenberg–Marquardt back-propagation neural network learning system, a well-established method, is utilized. The hidden layer employs sigmoid functions (tansig), as described in Equation (6), serving as the transfer function. Notably, the output layer does not incorporate an activation function, enabling the network output to be a continuous real number. The network would then directly output the predicted numerical values.

$$\begin{array}{c}\hfill \begin{array}{c}\hfill tanh\left(x\right)=\frac{2}{1+e^{-2x}}-1\end{array}\end{array}$$

(6)

Numerous techniques, as covered in the literature, can be used to estimate the size of the hidden layer [41]. One approach involves applying Kolmogorov’s theorem, as specified in Equation (7). Alternatively, a suitable range of values can be calculated based on an empirical formula, as outlined in Equation (8):

$$\begin{array}{c}\hfill \begin{array}{c}\hfill k=\sqrt{m+n}+a,a\in [1,10]\end{array}\end{array}$$

(7)

$$\begin{array}{c}\hfill \begin{array}{c}\hfill k=2n+1.\end{array}\end{array}$$

(8)

In this scenario, n represents the total number of input variables, m indicates the number of output variables, and k denotes the size of the hidden layer. The model’s inputs comprise the zone’s previous temperature, control action variables such as the supply air’s temperature and mass flow rate, and disturbance variables that exert significant influence on thermal behavior. These variables encompass the temperature of the four adjacent zones, the outdoor air temperature, the air mass flow from infiltration and uncontrolled natural ventilation, as well as the overall internal heat from humans and electrical devices. The model’s output is the zone’s temperature. Given that m equals 1 and n is set to 11, finding the appropriate size of the hidden layer is accomplished by assessing experimental results across a range of k values, spanning from 5 to 23. The MSE is employed to quantify the disparity between the actual and predicted values by squaring the error values and subsequently computing the mean of all errors. Throughout the neural network learning phase, the algorithm iteratively determines the optimal weights (${\mathbf{W}}^h$, W^o) and biases (${\mathbf{B}}^h$, B^o) to minimize the MSE, as calculated according to Equation (9):

$$\begin{array}{c}\hfill \begin{array}{c}\hfill \mathit{MSE}=\frac{1}{N}\sum _{i=1}^N{(y_i-\widehat{y_i})}^2\end{array}\end{array}$$

(9)

where

• $y_i$: the simulated or measured data;
• $\widehat{y_i}$: the predicted data from the ANN;
• N: N expresses the number of simulated or measured data.

It is crucial to utilize a dataset that reflects the building’s location and the specific case study, as well as one that encompasses the entire operating range of the plant in order to ensure accurate predictions. Nonlinear neural networks frequently face difficulties when attempting to make projections beyond their training data, as noted in Ref. [42]. Neural models are trained utilizing data obtained from a regular running plant with either closed-loop or open-loop control [43]. In this study, we generated the data using EnergyPlus DTS, as shown in Figure 1. These data were first stored and then used to train the ANN, which is our approach to black-box modeling.

To facilitate the training and validation of the ANNs under study, the data gathered from the simulation were partitioned into three distinct sets, following the recommendation provided by Ref. [44]. These sets include a training set (comprising 70% of the data), a validation set (which contains 15% of the data), and a test set (also encompassing 15% of the data). In this scenario, the chosen ANN model is the one associated with the lowest MSE, with 23 neurons in the hidden layer, where MSE = 0.0011362. This selection ensures a high level of predictive reliability, as the correlation between the ANN predictions and EnergyPlus simulations, as indicated by the chosen model, is approximately 1. This high correlation value signifies a very strong association, as illustrated in Figure 3.

3.2. MPC

To predict the area’s future temperature response, the trained ANN model was integrated into the MPC algorithm. By integrating a dynamic model into the controller, MPC facilitates efficient control over highly complex industrial processes. This integration enables the minimization of a cost function J across a finite prediction horizon, while also enabling real-time prediction of future process behavior. An optimization method that takes into account limitations on the system’s capabilities and control states is used to determine the ideal control input u. The control law can be expressed mathematically as in Equation (10). Within this context, various elements are integral to the system’s dynamics. The output of the system, denoted as $y\left(.\right)$, reflects its current state, while $y_r\left(.\right)$ represents the desired output trajectory. The coefficient Q modulates the importance assigned to the disparity between actual and desired outputs, reflecting their relative significance. Conversely, coefficient R regulates the penalty imposed on input variables, governing their amplitude during system operation. The neural network model of the system, encapsulated by $f_{NN}\left(.\right)$, offers an approximation of its behavior, facilitating predictive analysis. Optimal control input, designated as $u\left(.\right)$, steers the system towards desired setpoints, adjusting its operational parameters as necessary. These components collectively contribute to the system’s functioning and control mechanisms.

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill & \underset{u}{minimize}J\left(y,u\right)=\hfill \\ \hfill & \sum _{k=0}^{N-1}\left({\left(y\left(k\right)-y_r\left(k\right)\right)}^T·Q·\left(y\left(k\right)-y_r\left(k\right)\right)+u{\left(k\right)}^T·R·u\left(k\right)\right)\hfill \\ \hfill & subjectto:\hfill \\ \hfill & y\left(k+1\right)=f_{NN}\left(y\left(k\right),u\left(k\right),p\left(k\right)\right),\hfill \\ \hfill & y\left(0\right)=y_0,\hfill \\ \hfill & u\left(k\right)\in U,\forall k\in \left[0,N-1\right]\hfill \\ \hfill & y\left(k\right)\in X,\forall k\in \left[0,N\right]\hfill \end{array}\end{array}$$

(10)

At every time step k, the optimization algorithm predicts the future path of the state variables for a control horizon reaching $K+Nu$. It then executes the initial phase of the optimal control strategy. Following this, the system is sampled once more to initiate the optimization loop, considering the latest process state. This iterative approach integrates the actual measured state variable, thereby reducing potential errors resulting from differences between the model and actual conditions. In Figure 4, we observe two consecutive iterations of the MPC. On the left-hand side, the depiction illustrates the outcomes of the initial iteration, while the right-hand side showcases the subsequent iteration. In the latter, distinct visual elements highlight the progression of the MPC process. More specifically, the representation illustrates predictive trajectories of future system states and optimal control actions, shown in shades of gray and mustard at the previous iteration.

In contrast, in the new iteration, predicted values are depicted in red, predicted optimal control actions in green, applied control in blue, and the true measured system state variable in orange. This delineation allows for a clear distinction between the predicted and actual system behavior. Moreover, the visualization highlights the iterative nature of the MPC approach, with subsequent iterations incorporating updated predictions and optimizations based on real-time feedback.

3.3. PYNQ Implementation

MPC has been implemented in FPGAs in several studies. In Ref. [45], a novel matrix inversion method and circuit design were proposed to conduct MPC experiments within an embedded system. Another study adopted an MPC controller based on ellipsoidal sets, solving real-time optimization challenges using FPGA hardware [46]. The paper delved into the utilization of MPC to track the reference trajectory of the unmanned aerial vehicle. They proposed a DNN-based MPC scheme, with the implementation of the proposed method on a field FPGA using hardware-in-the-loop simulations [47]. Another study implemented Finite Control Set-MPC for power electronic systems using FPGAs, considering resource utilization and performance evaluation [48]. The deployment of long-horizon linear MPC on FPGAs was proven for regulating different power electronic systems in research [49]. Collectively, these papers illustrate the successful incorporation of MPC into FPGAs across a spectrum of control applications.

This optimization problem was then implemented in the PYNQ, an FPGA board designed to facilitate the utilization of platforms for adaptive computing. Designers can leverage programmable logic and microprocessors to develop more powerful and innovative electronic devices, utilizing the Python programming language and libraries. IpOpt [50] and CasADi [51] were used to address the optimization challenges within the MPC algorithm. Their source files were built and incorporated into the FPGA. EnergyPlus measures the current state and disturbance variables required for system control at each time step. The FPGA receives these data from the DTS to determine the optimal control action. Subsequently, the computed control values are transmitted to the DTS. The MQTT protocol handles the communication between the PYNQ board and the DTS sensors.

Figure 5 illustrates the communication process between the simulator and the PYNQ device. Initially, the simulator publishes data on the topics “Setpoint Temperature” and “Measured variables”. Subsequently, it subscribes to the “Optimal control” topic to receive control values. On the other hand, the PYNQ device subscribes to the “Setpoint Temperature” and “Measured variables” topics. Upon receiving the necessary data, the algorithm, running in the PYNQ, computes the optimal control value aimed at minimizing the disparity between the room temperature and the setpoint, all while minimizing energy consumption. Once the optimal control value is computed, the PYNQ publishes it on the “Optimal control” topic. The simulator retrieves this value, applies it, and then reevaluates the new variable values for the subsequent optimization iteration.

The choice of using EnergyPlus, a simulation tool, was influenced by the unavailability of a real building for implementing the solution proposed in this work. On the right-hand side of Figure 6 is the test bed designed to evaluate our solution. Positioned at the bottom is the PYNQ board, where the optimization algorithm operates in a continuous loop. Data transmission is facilitated by the MQTT protocol, with the display providing real-time feedback on the success or failure of transmission. On the simulator side, we showcase the optimal control value alongside the room temperature predicted by our algorithm, both of which are subsequently recorded. Conversely, on the other side, we display all measured variables essential for temperature prediction and energy optimization required to achieve the setpoint temperature.

4. Results

To validate the effectiveness of this control strategy, a comparative analysis was conducted between the NNMPC and the On/Off control law. According to the On/Off control law, the HVAC system operates at full capacity. For heating, it maintains a supply mass flow rate of 0.1 kg/s and a supply temperature of 50 °C. For cooling, it sustains a supply mass flow rate of 0.3 kg/s and a supply temperature of 13 °C. This process continues until the temperature surpasses the heating setpoint or falls below the cooling setpoint. The control law employs a 1 min sampling time, which aligns with the lowest time step available in EnergyPlus simulations. The building was simulated using EnergyPlus and was located in Casablanca, Morocco. The study considered two different years, 2006 and 2017, with outside temperature data shown in Figure 7, and the room temperature data applying the On/Off control strategy in Figure 8a,b.

On the other hand, the thermal mass of construction materials causes disturbances that have slow dynamics and a high moment of inertia. Consequently, the NNMPC controller runs with a 10 min sample period. Between 0 and 0.1 kg/s is the range of the supply mass flow rate, and 50 °C is the temperature at which the supply air is kept for heating and cooling. Furthermore, the supply mass flow rate changes from 0 to 0.3 kg/s for cooling, with the supply air temperature set to 13 °C.

Temperature predictions from ANN are closely aligned with EnergyPlus calculations. Thanks to the NNMPC control strategy, EnergyPlus temperature measurements are managed consistently to stay, most of the time, around the target temperature (a range of approximately ±0.5 °C); see Figure 9 and Figure 10. Moroccan thermal regulations provide specific guidelines regarding temperature settings for heating and air conditioning systems. According to these regulations, the designated temperature setpoint for heating is 20 °C, while for air conditioning, it is set at 26 °C [52]. Consequently, the range between 20 °C and 26 °C delineates our defined thermal comfort zone. In addition to the prescribed comfort range, we have incorporated an acceptable discomfort zone of 0.5 °C above the air conditioning setpoint and below the heating setpoint. This intentional extension allows for a degree of flexibility, particularly within our predictive control methodology.

Figure 11 and

Table 1. Heating and cooling comparison.

			Heating			Cooling
			NNMPC (kWh)	On/Off (kWh)	Savings (%)	NNMPC (kWh)	On/Off (kWh)	Savings (%)
2006	PYNQ	January	78.64	119.88	34.40	0.00	0.00	-
		February	50.61	83.21	39.18	0.00	0.00	-
		March	21.12	38.60	45.29	0.00	0.00	-
		April	34.01	59.46	42.80	0.00	0.00	-
		May	1.71	5.51	69.00	0.00	0.00	-
		June	0.00	0.00	-	1.08	3.06	64.60
		July	0.00	0.00	-	33.09	58.11	43.05
		August	0.00	0.00	-	61.50	93.96	34.55
		September	0.00	0.00	-	80.65	113.62	29.02
		October	0.00	0.00	-	30.67	58.76	47.80
		November	7.23	15.12	52.19	14.86	29.03	48.81
		December	46.72	83.53	44.07	0.00	0.00	-
		Total	240.04	405.31	40.78	221.86	356.54	37.77
	Desktop	January	78.59	119.88	34.44	0.00	0.00	-
		February	50.61	83.21	39.18	0.00	0.00	-
		March	21.10	38.60	45.33	0.00	0.00	-
		April	34.08	59.46	42.69	0.00	0.00	-
		May	1.72	5.51	68.78	0.00	0.00	-
		June	0.00	0.00	-	1.07	3.06	64.95
		July	0.00	0.00	-	33.09	58.11	43.05
		August	0.00	0.00	-	61.50	93.96	34.55
		September	0.00	0.00	-	80.65	113.62	29.02
		October	0.00	0.00	-	30.67	58.76	47.80
		November	7.23	15.12	52.19	14.86	29.03	48.81
		December	46.72	83.53	44.07	0.00	0.00	-
		Total	240.04	405.31	40.78	221.85	356.54	37.78
2017	PYNQ	January	188.74	238.40	20.83	0.00	0.00	-
		February	119.01	156.38	23.90	0.00	0.00	-
		March	70.00	100.48	30.34	0.00	0.00	-
		April	4.64	10.95	57.57	0.00	0.00	-
		May	2.12	5.06	58.02	0.00	0.00	-
		June	0.00	0.00	-	0.00	0.00	-
		July	0.00	0.00	-	42.31	67.83	37.61
		August	0.00	0.00	-	58.95	90.80	35.08
		September	0.00	0.00	-	139.65	173.93	19.71
		October	0.00	0.00	-	95.65	134.53	28.90
		November	0.03	0.00	-	33.23	52.35	36.53
		December	80.34	113.58	29.27	0.00	0.00	-
		Total	464.89	624.86	25.60	369.78	519.43	28.81
	Desktop	January	188.68	238.40	20.86	0.00	0.00	-
		February	119.08	156.38	23.85	0.00	0.00	-
		March	69.99	100.48	30.35	0.00	0.00	-
		April	4.63	10.95	57.71	0.00	0.00	-
		May	2.12	5.06	58.03	0.00	0.00	-
		June	0.00	0.00	-	0.00	0.00	-
		July	0.00	0.00	-	42.31	67.83	37.62
		August	0.00	0.00	-	58.87	90.80	35.17
		September	0.00	0.00	-	139.86	173.93	19.59
		October	0.00	0.00	-	95.66	134.53	28.89
		November	0.03	0.00	-	33.11	52.35	36.75
		December	80.47	113.58	29.16	0.00	0.00	-
		Total	465.01	624.86	25.58	369.81	519.43	28.80

represent the energy consumed by heating and cooling for each month of the years 2006 and 2017, applying the On/Off control method and the NNMPC method, respectively, with the NNMPC calculated in the Desktop and PYNQ. For both years, September and January represent the most energy-intensive months for HVAC systems, in both control modes. In September 2017, we had a consumption of 139.65 kWh versus 173.93 kWh for NNMPC control and On/Off mode, respectively, which represents a reduction of 19.71%. For January, we had a consumption of 188.74 kWh versus 238.40 kWh for NNMPC control and On/Off mode, respectively, which represents a reduction of 20.83%. This energy reduction is close to that provided by the computer, where it represents 19.59% for September and 20.85% for January. During the year 2006, in January 2006, consumption was 78.64 kWh compared with 119.88 kWh for NNMPC control and On/Off mode, respectively, representing a reduction of 34.4%. For September 2006, consumption of 80.65 kWh versus 113.62 kWh for NNMPC control and On/Off mode, respectively, represents a reduction of 29.02%. This energy reduction is the same as the one provided by the computer.

For an annual analysis, in the year 2006, we had a heating consumption of 240.04 kWh versus 405.31 kWh for NNMPC control and On/Off mode, respectively, representing an annual reduction in heating energy consumption of 40.78%. For cooling consumption, it was 221.86 kWh compared with 356.54 kWh for NNMPC control and On/Off mode, respectively, representing a reduction of 37.77%. For the year 2017, we had a cooling consumption of 369.78 kWh versus 519.43 kWh for NNMPC control and On/Off mode, respectively, representing an annual reduction in cooling energy consumption of 28.81%. For heating consumption, it was 464.89 kWh versus 624.86 kWh for NNMPC control and On/Off mode, respectively, representing a reduction of 25.60%; see Figure 12 and Table 1.

Figure 13 illustrates the room temperature fluctuating within a range, primarily between 20 °C and 26 °C. However, it is noteworthy that the NNMPC, deployed on PYNQ, tends to shift the room temperature into the discomfort zone more frequently compared to the On/Off method. Specifically, in 2017, we observe that, under NNMPC control, 10.72% of the time, the temperature falls below 20 °C, with a deviation of 0.85% on average, which represents 0.17 °C, and with a maximum deviation of 7.80%, which represents 1.55 °C. For 14.77% of the time, it exceeds 26 °C, with a deviation of 0.91% on average, which represents 0.24 °C, and with a maximum deviation of 5.85%, which represents 1.16 °C.

Regarding the Desktop implementation, the values are notably closer, with 10.58% below 20 °C, with a deviation of 0.80% on average, which represents 0.16 °C, and with a maximum deviation of 4.17%, which represents 0.83 °C. Additionally, we have 14.86% above 26 °C, with a deviation of 0.89% on average, which represents 0.23 °C, and with a maximum deviation of 5.67%, which represents 1.13 °C. In contrast, with the On/Off method, the discomfort zone occurrences are lower, with only 2.53% below 20 °C, with a deviation of 0.68% on average, which represents 0.13 °C, and with a maximum deviation of 3.73%, which represents 0.74 °C. For 1.95% of the time, it exceeds 26 °C, with a deviation of 0.41% on average, which represents 0.1 °C, and with a maximum deviation of 2.82%, which represents 0.56 °C. Moreover, the NNMPC breaches the critical threshold of 19.5 °C only 0.2% of the time and goes above 26.5 °C merely 0.92% of the time, which remains within acceptable limits. Considering the predictive nature of the NNMPC, such deviations can be accommodated without significant inconvenience.

In the 2006 data, we observe that, under NNMPC control, 14.38% of the time, the temperature falls below 20 °C, with a deviation of 0.86% on average, which represents 0.17 °C, and with a maximum deviation of 6.79%, which represents 1.35 °C. For 12.04% of the time, it exceeds 26 °C, with a deviation of 0.97% on average, which represents 0.25 °C, and with a maximum deviation of 6.16%, which represents 1.23 °C. Regarding the Desktop implementation, the values are notably closer, with 14.41% below 20 °C, with a deviation of 0.82% on average, which represents 0.16 °C, and with a maximum deviation of 4.03%, which represents 0.8 °C. Additionally, we have 12.04% above 26 °C, with a deviation of 0.97% on average, which represents 0.25 °C, and with a maximum deviation of 6.16%, which represents 1.23 °C. In contrast, with the On/Off method, the discomfort zone occurrences are lower, with only 1.66% below 20 °C, with a deviation of 0.38% on average, which represents 0.07 °C, and with a maximum deviation of 2.56%, which represents 0.51 °C. For 1.52% of the time, it exceeds 26 °C, with a deviation of 0.4% on average, which represents 0.1 °C, and with a maximum deviation of 2.53%, which represents 0.5 °C. Moreover, the NNMPC breaches the critical threshold of 19.5 °C only 0.32% of the time and goes above 26.5 °C merely 1.02% of the time, which remains within acceptable limits.

Figure 14 depicts the deviation distribution of both the On/Off control law and NNMPC for the years 2006 and 2007. Additionally, it illustrates the deviation distribution for the computer implementation of the NNMPC solution and PYNQ. The deviation calculation is based on Equation (11). In this context, the negative portion of the deviation distribution signifies instances falling outside the defined comfort zone. Specifically, during the heating season, negative values indicate deviations below the setpoint of 20 °C, indicating situations where room temperature falls below the desired level. Conversely, in the cooling season, negative values signify deviations exceeding the setpoint of 26 °C, reflecting instances where the temperature surpasses the desired threshold. Thus, negative values in the deviation distribution directly correspond to discomfort, manifesting as sensations of cold during winter and heat during summer. The deviation can be computed using the following equation:

$$\begin{array}{c}\hfill \mathrm{deviation}\left(i\right)=\left\{\begin{array}{cc}20-\mathrm{temperature}\left(i\right),\hfill & \mathrm{if}\mathrm{setpoint}\left(i\right)=20\mathrm{and}\mathrm{control}\mathrm{on}\hfill \\ \mathrm{temperature}\left(i\right)-26,\hfill & \mathrm{if}\mathrm{setpoint}\left(i\right)=26\mathrm{and}\mathrm{control}\mathrm{on}\hfill \\ \mathrm{NaN},\hfill & \mathrm{otherwise}\hfill \end{array}\right..\end{array}$$

(11)

Here, i represents the index of the deviation. This equation defines the computation of deviation based on the specified conditions for the temperature setpoints and control status. We observe from Figure 14 that the NNMPC method confines room temperature to within ±0.5 °C of the setpoint for both heating and cooling in 93% to 98% of cases. In contrast, the On/Off method surpasses the setpoint by 1.5 °C to 2.5 °C for heating and drops 2.5 °C to 3.5 °C below the setpoint for cooling. These deviations represent significant fluctuations in room temperature, potentially causing discomfort for occupants despite remaining within the established comfort zone. Conversely, the NNMPC method maintains a certain stability of room temperature around the setpoint, whether for heating or cooling.

The term PMV stands for Predicted Mean Vote. It is a metric used in thermal comfort analysis to predict how a person will perceive the thermal environment. PMV is based on a model developed by Fanger in the 1970s [53,54] and is widely used in building design, HVAC systems, and indoor environmental quality assessment.

The PMV index quantifies the predicted average thermal sensation of a large group of people exposed to a specific indoor environment. It takes into account various factors such as air temperature, radiant temperature, air speed, humidity, and clothing insulation. It operates on a 7-level thermal sensation scale, ranging from $-3$ to +3, as depicted in Figure 15.

A PMV of 0 indicates a neutral thermal sensation, while values closer to +1 represent slightly warm conditions, and values closer to $-1$ suggest slightly cool conditions. A PMV of +2 signifies warm conditions, and $-2$ indicates cool conditions. Extremes of thermal sensation, such as PMV values of +3 or $-3$, correspond to perceived hot or cold environments, respectively. Understanding and maintaining PMV within acceptable ranges are crucial for ensuring occupant comfort and productivity in indoor spaces. In indoor environmental quality assessment, three main categories are commonly used to gauge occupant comfort. In Category I, environments are considered highly satisfactory when the PDD is 10% or lower and when the PMV falls within the range of $-0.5$ to +0.5. In Category II, satisfaction levels are moderately satisfactory, with PPD ranging between 10% and 25%. PMV is deemed acceptable when it falls within the range of $-1$ to $-0.5$ or from +0.5 to +1. In Category III, environments are deemed unacceptable if the PPD exceeds 25%. PMV values beyond $-1$ or above +1 are considered unsatisfactory in this category [55].

Clothing insulation and metabolic rate have a strong influence on thermal comfort [56]. Clothing insulation specifies the level of insulation worn by occupants in a building. The thermal resistance of clothing materials directly influences thermal comfort and energy consumption within the building. During colder months, such as December to April, higher insulation values, ranging from 1 to 1.2 clo, are prescribed. Conversely, during warmer months, such as June to October, lower insulation values, ranging from 0.4 to 0.5 clo, are recommended, reflecting the lighter garments worn during warmer temperatures. For the months of May and November, average insulation values ranging from 0.7 to 0.8 clo are used, with $1\mathrm{clo}=0.155{\mathrm{m}}^2\mathrm{K}{\mathrm{W}}^{-1}$. By adjusting clothing insulation levels based on seasonal variations, occupants experience comfort throughout the year, contributing to a conducive indoor environment and overall building efficiency.

The internal gain of occupants within the space fluctuated throughout the day, totaling 131.8 W. This value was subject to modification by a fractional factor across distinct time intervals. The distribution of these factors delineates the fluctuating impact of internal gains throughout the day. Starting from the onset of the day until 06:00, the internal gain factor stood at 0.67. Between 06:00 and 07:00, the factor decreased to 0.45, indicating a reduction in internal gains. Continuing from 07:00 to 08:00, the factor further declined to 0.27. From 08:00 until 19:00, the factor stabilized at 0.3, representing a relatively steady level of internal gains during daytime hours. During the evening hours, from 19:00 to 21:00, the factor decreased to 0.21, reflecting diminished internal gains. Between 21:00 and 22:00, the factor experienced a slight increase to 0.33, suggesting a minor resurgence in internal gains. Finally, from 22:00 until midnight, the factor reverted to 0.67.

Natural ventilation, quantified as 1 ACH or 1 volume per hour (V/h), is a fundamental aspect of building design, contributing to indoor air quality and thermal comfort. This ventilation rate indicates how often the air in a specific zone is replaced by fresh outside air. A ventilation rate of 1 ACH or 1 V/h means that the entire volume of the space is renewed by outside air every hour. These ventilation strategies are essential for maintaining optimal indoor environmental conditions by expelling pollutants, regulating humidity levels, and promoting thermal comfort. In addition, natural ventilation promotes energy efficiency by reducing reliance on mechanical systems, in line with sustainable building practices. Implementing natural ventilation at a rate of 1 ACH or 1 V/h underscores a balanced approach to enhancing occupant well-being while promoting environmental stewardship in building design and operation. Figure 16 and Figure 17 depict the value and distribution of the PMV, respectively, for both the On/Off control law and NNMPC for the years 2006 and 2007.

Table 2. Percentage of Predicted Mean Vote (%).

		NNMPC (%)		On/Off (%)
		PYNQ	Desktop	Desktop
2006	−3.0 < PMV < −1.0	0.00	0.00	0.00
	−1.0 < PMV < −0.5	0.00	0.00	0.00
	−0.5 < PMV < 0.5	72.35	72.45	83.75
	0.5 < PMV < 1.0	27.14	27.04	16.07
	1.0 < PMV < 3.0	0.51	0.51	0.17
2017	−3.0 < PMV < −1.0	0.00	0.00	0.00
	−1.0 < PMV < −0.5	0.20	0.20	0.22
	−0.5 < PMV < 0.5	64.98	65.06	76.77
	0.5 < PMV < 1.0	32.80	32.75	22.50
	1.0 < PMV < 3.0	2.01	2.00	0.51

illustrates the distribution of PMV for the years 2006 and 2017 categorized by control strategies and implementation platforms. The table structure consists of four rows representing different PMV thresholds ($-3.0$ < PMV < $-1.0$, $-1.0$ < PMV < $-0.5$, $-0.5$ < PMV < 0.5, 0.5 < PMV < 1.0, and 1.0 < PMV < 3.0) and three columns displaying the distribution percentages under the NNMPC and On/Off control strategies implemented on both the PYNQ and Desktop platforms.

For the years 2006 and 2017, the table presents the percentage distribution of instances where the PMV falls within specified intervals for different control strategies and platforms. For the year 2006, no instances are recorded where PMV falls below $-0.5$ across all control strategies and platforms. However, for the year 2017, only 0.20%, 0.20%, and 0.22% of PMV values for NNMPC on PYNQ, NNMPC on Desktop, and On/Off control on Desktop, respectively, fall below $-0.5$. Conversely, for PMV values between $-0.5$ and 0.5, the percentages are notably high, standing at 72.35%, 72.45%, and 83.75% for NNMPC on PYNQ, NNMPC on Desktop, and On/Off control on Desktop, respectively, in 2006. In 2017, the percentages remain significant, with values of 64.98%, 65.06%, and 76.77% for the same respective categories. Additionally, for PMV values between 0.5 and 1.0, the percentages in 2006 are 27.14%, 27.04%, and 16.07%, respectively, while in 2017, they amount to 32.80%, 32.75%, and 22.50%. PMV values exceeding 1.0 also show substantial differences, with percentages ranging from 0.17% to 2.01% across different strategies and platforms in both 2006 and 2017. Regarding the maximum and minimum PMV values, the data highlight a variation between the two years, with maximum PMV values ranging from 1.11 to 1.34 and minimum PMV values ranging from $-0.43$ to $-0.83$ across the platforms and strategies considered; see

Table 3. Maximum and minimum Predicted Mean Vote value.

		PMV
		NNMPC		On/Off
		PYNQ	Desktop	Desktop
2006	Max	1.26	1.26	1.11
	Min	−0.48	−0.43	−0.49
2017	Max	1.34	1.34	1.27
	Min	−0.81	−0.81	−0.83

.

The analysis reveals that, on the whole, the two control techniques converge on a value for PMV around the threshold of Category I, where environments are considered very satisfactory. However, upon PMV surpassing 1, the On/Off method marginally outperforms the NNMPC solution in meeting the thermal comfort criterion of PMV. It is worth noting that the optimal PMV values, which closely approach 0, tend to occur around a temperature of 22.5 °C. Remarkably, this temperature sits above the RTCM setpoint for heating and below it for cooling. Furthermore, the On/Off method adeptly steers the temperature closer to this optimal point (22.5 °C), thereby elucidating its superior performance in ensuring thermal comfort. However, the classic control method requires more energy to achieve its objectives, as evidenced by the Kernel Density Estimate (KDE) plots in Figure 18. These plots offer insights into the distributions and relationships between the MSE and sensible energy needs for the NNMPC and On/Off control strategies across both years (2006 and 2017). Here, we aimed to assess the influence of the sensible thermal energy delivered by our HVAC system on the room temperature. In essence, we sought to quantify the change in room temperature following the supply of energy by the HVAC system. The MSE calculation method used here computes the average of the squares of the differences between the room temperature before and after the HVAC system’s energy supply. This approach enables us to understand the temperature variation induced by the HVAC system when it provides energy in the form of a mass flow rate of hot or cold air as required. The findings affirm that the NNMPC control strategy not only markedly diminishes our energy needs for heating and cooling to stay within the comfort zone, as demonstrated by the study’s outcomes, but also ensures that room temperature remains closely aligned with the setpoint, thereby guaranteeing consistent thermal comfort throughout the control process.

5. Discussion

Several initiatives have successfully reduced HVAC system energy consumption while ensuring occupant thermal comfort; see

Table 4. Summary of studies on building control strategies.

Study	Objectives	Methods	Results
Bastida et al. [16]	Temperature regulation.	PI controller.	8% energy savings for heating.
Zhao et al. [57]	Improved energy consumption with maintained thermal comfort.	EnergyPlus MPC.	Substantial energy reductions (28.9% heating, 2.7% cooling).
Aruta et al. [58]	Enhance energy efficiency. Minimize heating energy costs based on weather forecasts.	MPC with ANNs and ML.	Significant daily energy savings of 26% for heating.
Yang et al. [33]	Emphasize performance building automation.	MPC with adaptive system based on ML.	Substantial savings in cooling energy (58.5% in the office, 36.7% in the lecture theater).
Ferreira et al. [59]	Implement radial basis function neural networks for thermal comfort and energy savings.	Radial basis function neural networks.	Estimated energy savings exceeding 50%.
Jazizadeh et al. [60]	Develop a comprehensive framework for enhancing occupants’ thermal comfort using a participatory sensing approach.	Fuzzy predictive model.	39% reduction in daily average airflow rates.
Naseem et al. [61]	Compare EnergyPlus MPC, the basic On/Off strategy, and SMC.	EnergyPlus MPC, Sliding Mode Control.	In the summer, MPC used 14.67% less energy than a basic On/Off system controller and saved 11.94% more energy than SMC. In the winter, the MPC used 19.89% less energy than SMC and 17.20% less than the On/Off controller.
Dong et al. [62]	Reduce energy consumption.	NMPC.	Measured energy reductions (30.1% in heating, 17.8% in cooling).
Mohamed Alqadi et al. [63]	Reduce cooling energy consumption.	Occupancy-based strategy.	Noteworthy 59% reduction in energy consumption.
Boudier et al. [64]	Reductions in energy consumption.	Adaptive controller.	Achieved reductions in energy consumption (12.5% in winter, 15.3% in summer).
Qin et al. [27]	Achieve building energy savings.	Dynamic programming.	35.1% reduction in energy consumption and emissions.
Fu et al. [28]	Optimize building’s cooling water system.	Multi-agent deep reinforcement learning.	11.1% improvement compared to rule-based control.
Present study	Improve energy consumption with maintained thermal comfort. Optimize the building’s cooling and heating system. Reduce energy consumption.	NNMPC.	Year 2006, an annual reduction in heating energy consumption of 40.8% and 37.8% for cooling energy consumption when compared to conventional On/Off control techniques. Year 2017, an annual reduction in cooling energy consumption of 28.8% and 25.6% for heating energy needs when compared to conventional On/Off control techniques.

. These studies typically employ their proposed solutions and compare them with basic On/Off control techniques. Replicating exact circumstances for comparison analysis is a real problem for experimental studies. The limitation arises from difficulties in reproducing precise environmental factors that may influence the thermal performance of a building. In contrast, simulation could provide a valuable avenue for overcoming this challenge by allowing researchers to recreate and control various conditions.

In the work conducted by Ref. [16], based on heat transfer concepts similar to electrical systems, researchers created reduced-order systems using a frequency response technique. The findings showed that using a PI controller to regulate temperature effectively might save around 8% of energy when compared to standard On/Off control, all while preserving interior comfort. EPMPC was developed in Ref. [57] and achieved substantial reductions in energy consumption during a one-week simulation, with heating energy reduced by 28.9% and cooling energy by 2.7%. Unlike traditional rule-based control systems, these enhancements were achieved without sacrificing occupant thermal comfort. The subsequent study by Ref. [58] aimed to improve the energetic performance of a building situated in Benevento, Italy. To regulate the NZEB’s heating system, they used a framework based on simulation and optimization that integrated ANNs and ML models inside MPC. This framework used weather forecasts to determine the ideal setpoint temperatures, hence minimizing heating energy expenses and discomfort. Taking comfort penalties into account, they produced the Pareto front and chose the best option. In comparison to a fixed setpoint control, experiments carried out over a typical heating day showed a considerable daily energy consumption reduction of 26%.

Building automation was the main objective of the study by Ref. [33], which evaluated the efficacy of an MPC system featuring adaptive ML-based control. The office and the theater were the two zones where this strategy was used, and the results were huge energy savings. In comparison to the initial control approach, they accomplished a 58.5% decrease in cooling energy usage within the office and a 36.7% drop in amphitheater air-conditioning power usage.

Implementing radial basis function neural networks, as proposed by Ref. [59], is an effective strategy for achieving both thermal comfort and energy savings in public buildings. The approach optimizes a cost function intended to reduce energy usage while preserving the required comfort levels, and it uses the PMV index to assess thermal comfort. This approach comprises three crucial components: the implementation of radial basis function neural networks for prediction, an energy consumption-minimizing cost function, and the utilization of a discrete branch and bound optimization method. The application of this predictive modeling method is anticipated to yield substantial energy savings, surpassing 50%, with a range spanning from 41% to 77%.

In the study conducted by Ref. [60], a comprehensive framework was developed to enhance occupants’ thermal comfort within HVAC operations. This framework is built upon several key components, including to gradually acquire customized thermal comfort profiles. A room-based distributed control strategy is incorporated into the process, distinct from traditional thermal zone-based approaches, and integrates seamlessly with legacy HVAC systems. This innovative approach reduced average airflow rates by a significant 39% on a daily basis, showcasing its efficacy in providing and maintaining thermal preferences based on the individual thermal comfort data of occupants.

The study conducted by Ref. [61] aimed to prioritize interior thermal comfort while developing energy-efficient control strategies for HVAC systems in non-domestic buildings. SMC, basic On/Off control, and MPC based on the EnergyPlus model were the control strategies employed and evaluated in this study. The EnergyPlus model-based MPC, utilizing the state-space model, outperformed other strategies in terms of energy efficiency. During summers, it demonstrated an 11.94% greater energy savings compared to SMC and, in comparison to the On/Off command, it consumed 14.67% less energy. Additionally, for a setpoint of 23 °C during winters, compared to the On/Off command, the MPC consumed 17.20% less energy, and it used 19.89% less energy than SMC. The PMV-based setpoints, computed using an ANN, proved effective in reducing power consumption by 3.48% when integrated into an On/Off controller. The research findings highlight the potential of an EnergyPlus model-based MPC as an energy-efficient control technique for HVAC systems in non-domestic buildings. The strategy not only outperformed SMC and the basic On/Off strategy during summers but also demonstrated substantial energy savings during winters, without compromising occupants’ thermal comfort.

The primary objective of the research conducted by Ref. [62] was to forecast occupant activity patterns and local weather in order to minimize energy usage and maintain room temperature setpoints. The study employed NMPC as a key strategy, showcasing significant measured energy reductions. During the heating season, the implemented NMPC resulted in a substantial 30.1% measured energy reduction compared to conventional scheduled temperature setpoints. Similarly, in the cooling season, there was a notable 17.8% reduction in energy consumption. These outcomes were obtained through experiments that lasted one week during the cooling season and two continuous months during the heating season. By leveraging occupant behavior predictions and local meteorological data, this approach effectively reduces energy consumption.

The goal of the study conducted by Ref. [63] was to lower buildings’ cooling energy usage. By utilizing a constant temperature setpoint based on the occupancy method, the suggested technique results in a noteworthy 59% reduction in energy consumption. This indicates the effectiveness of integrating occupancy information into the control strategy to achieve substantial energy savings in cooling systems for buildings.

The adaptive controller, in the study conducted by Ref. [64], demonstrated notable achievements in energy efficiency, with a 12.5% decrease in end-use energy for heating and a 15.3% reduction in summer. The study envisaged decentralized systems that inhabitants would control for climatic changes and personal preferences. In fact, consumers would be in charge of these systems rather than their being automatically governed. The overall level of comfort and energy use were affected differently by this decentralized strategy. The targeted temperature of the HVAC system might be modified by the adaptive building controller depending on the thermal feeling and comfort levels of a simulated person.

The study carried out by Ref. [27] focused on achieving building energy savings and emission reduction through a dynamic programming algorithm. The dynamic programming algorithm achieved an impressive 35.1% reduction in energy consumption and emissions against the baseline scenario with a room temperature set at 20 °C. This indicates that the proposed control algorithm surpassed the baseline scenario significantly in terms of energy efficiency. Nevertheless, the algorithm produced an even more spectacular reduction in energy usage, reaching 47.49%, when imposing sacrifice in comfort (1–2 °C under the pleasant temperature 37% of the time).

The study conducted by Ref. [28], proposed a multi-agent deep reinforcement learning method, MA-CWSC. The primary objective of this method was to enhance energy efficiency in the cooling water system. The experimental results demonstrated the effectiveness of the MA-CWSC method, and the energy-saving performance achieved by the proposed method demonstrates an improvement on the initial method of 11.1%. The energy-saving performance achieved by the proposed method was significantly superior to the rule-based control approach. Remarkably, the MA-CWSC method exhibited energy savings close to that of a model-based control method, with only a marginal 0.5% difference.

These significant energy savings are attributed, in part, to the shortcomings of standard HVAC system controls, which can result, among other things, from overly simplistic control algorithms or incorrectly configured setpoints [59]. However, achieving a truly meaningful comparison necessitates aligning critical factors, including climate information, the thermal model of the building, and all variables impacting its thermal behavior. The scarcity of information and data required for a direct comparison under identical conditions restricts researchers from evaluating and contrasting results within the unique context of each study. Differences in building models, climatic data, control periods, and other parameters make it challenging to draw definitive conclusions beyond the scope of each individual research initiative.

6. Conclusions

The approach for creating an MPC system driven by an ANN model to improve building energy efficiency and thermal comfort of occupants is presented in this research. To train the neural network model, the method involves generating a dataset using a DTS. Once trained, this model is used as the MPC model to predict future states of real systems.

The proposed nonlinear NNMPC, implemented on an FPGA, has shown considerable savings in thermal energy usage for both cooling and heating as compared to conventional On/Off control techniques. For the year 2006, the results indicate that the annual cooling energy consumption decreased by 37.8%, while the annual heating energy consumption showed an impressive annual reduction of 40.8%. In the subsequent year of simulation, 2017, the results indicate an annual reduction in heating energy consumption by 25.6% and a remarkable 28.8% annual reduction in cooling energy consumption. No instances were recorded where the PMV fell below $-0.5$ across all strategies and platforms. Conversely, a notable proportion (ranging from 65% to 83%) of PMV values fell between $-0.5$ and 0.5, indicating a high level of occupant comfort. Additionally, percentages for PMV values between 0.5 and 1.0 ranged from 16% to 33% for both years. Notably, the NNMPC system exhibited superior performance in maintaining occupants’ comfort within the specified range, requiring less energy while converging the PMV value around the threshold indicative of highly satisfactory environments. These findings underscore the effectiveness of the NNMPC system in substantially improving energy efficiency in buildings and the thermal comfort of occupants.

Enhancing energy reduction can be achieved through a synergistic integration of multiple strategies. By accurately discerning the presence of occupants through a presence detection module and forecasting their future presence based on habitual patterns, the system can dynamically adjust environmental controls to optimize energy usage. Moreover, the integration of natural ventilation during favorable outdoor weather conditions presents a complementary opportunity. By harnessing natural airflow and minimizing reliance on traditional heating and air-conditioning systems, the building can capitalize on environmental resources more efficiently. This integrated approach not only fosters energy efficiency but also mitigates the economic burden associated with conventional heating and cooling systems. By reducing energy consumption and operational costs, buildings can realize tangible savings while simultaneously reducing their carbon footprint.