Model Predictive Control Using an Artificial Neural Network for Fast-Charging Lithium-Ion Batteries

Abstract

The increasing computational complexity of Model Predictive Control (MPC) in battery systems limits its practical adoption, despite its potential for optimizing performance under dynamic operating conditions. To address this challenge, this study introduces an Artificial Neural Network-based MPC framework (MPCANN) tailored for VTC6 3Ah lithium-ion cells, aiming to reduce computational burdens while retaining predictive accuracy. The framework synergizes MPC’s predictive capabilities with the daptive learning of Artificial Neural Network (ANN) by training the ANN offline using MPC-derived input–output data. Validation against prior MPC results demonstrates MPCANN’s ability to replicate MPC behavior across temperatures, achieving strong alignment in current and temperature predictions. While state of charge (SoC) estimation accuracy requires refinement at elevated temperatures, the framework reduces computation time by 94% compared to traditional MPC, highlighting its efficiency. These results underscore MPCANN’s potential to enable real-time implementation of advanced battery control strategies, offering a pathway to balance computational efficiency with performance in adaptive energy systems.

1. Introduction

Lithium-ion batteries (LiBs) have become essential components in modern technology, powering a wide range of devices from portable electronics to electric vehicles (EVs) [1]. One of the most pressing challenges in the battery industry is the development of fast charging methods that maintain safety and minimize degradation [2]. The lengthy charging times of EVs [3], in particular, have been identified as a significant barrier to their widespread adoption, underscoring the importance of developing efficient and fast charging stations [4]. However, high-rate charging presents a complex set of challenges [5]. It involves balancing the need for rapid energy transfer against the risks of accelerated aging, increased thermal gradients, and reduced battery lifespan [6,7,8]. Fast charging exacerbates spatial inhomogeneities in ion concentration and electrochemical reactions within battery cells [9,10]. These localized disparities can lead to lithium plating, dendritic growth, and mechanical stress concentrations, significantly increasing safety risks such as internal short circuits [11] and thermal runaway [12,13,14,15,16]. Furthermore, the interplay between rapid lithium-ion intercalation and electrolyte decomposition at high currents creates gas evolution and electrode swelling, compromising structural integrity over time [9]. These issues are exacerbated by extreme temperature conditions [17], which can amplify reaction heterogeneity and accelerate failure mechanisms.These issues are exacerbated by extreme temperature conditions, which can significantly impact battery performance and longevity [18].

To address these challenges, advanced control strategies have become increasingly crucial in battery management systems [19,20]. Model Predictive Control (MPC) has emerged as a promising approach for optimizing battery performance [21,22,23,24,25]. MPC is an advanced control strategy that uses a model of the system to predict future states and optimize control actions over a receding horizon. By considering multiple objectives and constraints simultaneously, MPC can effectively balance charging performance, thermal management, and battery health. However, the practical implementation of MPC faces significant hurdles due to its high computational complexity and resource requirements [26,27,28]. While hybrid approaches combining MPC with machine learning have been proposed to address these challenges [23,29], they often face trade-offs between computational efficiency, generalizability across temperature ranges, and accuracy in state of charge (SoC) estimation.

Parallelly, Artificial Neural Networks (ANNs) have demonstrated high accuracy in battery estimation tasks [30,31,32,33,34]. ANNs can effectively model complex nonlinear relationships between battery parameters and states, enabling precise estimation of critical metrics such as state of charge (SOC) and state of health (SOH). Moreover, ANNs can subsequently reduce the complexity of a task and execute it without requiring any mathematical equations, thus minimizing the computational complexity and resource demands. This makes ANNs particularly suitable for real-time applications in battery management systems, where rapid and accurate estimations are crucial for optimal performance and safety. The ability of ANNs to learn from historical data and adapt to changing battery characteristics over time further enhances their effectiveness in battery management applications.

Therefore, this study introduces an innovative concept called Artificial Neural Network-based Model Predictive Control (MPCANN), specifically designed for VTC6 3Ah 18650-type lithium-ion cells. The MPCANN framework integrates the predictive capabilities of MPC with the adaptive learning features of Artificial Neural Networks (ANNs). By training the ANN offline using input–output data derived from an MPC algorithm, this approach aims to significantly reduce computational demands while preserving the benefits of predictive control. The battery model employed in this study was developed in a previous research effort [35]. It utilizes a comprehensive electro-thermal model of a 3Ah cylindrical battery including a lifetime estimation tool, which was meticulously validated at different ambient temperatures (−10 °C, 10 °C, 25 °C, 35 °C, 45 °C, and 60 °C) in prior work [35]. By leveraging this rigorously tested framework, MPCANN aims to bridge the gap between computational practicality and control precision—a persistent challenge in battery management systems (BMS) that often forces compromises between passive balancing’s simplicity and active balancing’s efficiency.

This paper is structured as follows: Section 2 details the battery feature. Section 3 presents the complete electro-thermal and lifetime model. Section 4 covers the combined MPCANN models. Section 5 discusses the MPCANN results. Finally, Section 6 provides the conclusions of the study.

2. Battery Feature

The batteries used in this study were cylindrical VTC6 18650-type lithium-ion cells (LiBs) with a capacity of 3 Ah, manufactured by Sony in China (Figure 1). These cells feature a Li(NiMnCo)₁/₃O₂ cathode and a graphite anode, with an average mass recorded at 46.6 g. Their nominal capacity and voltage were 3 Ah and 3.7 V, respectively. In this paper, the C-rate (C) is defined as 1C = 3 A.

3. Model Development

3.1. Model Methodology

This paper employs a complete battery model by integrating and validating specialized sub-models into a unified modeling framework. This framework incorporates electrical, thermal, and aging models, as illustrated in Figure 2. The entire model was created using the MATLAB/Simulink® R2024b platform. The electro-thermal component simulates both the electrical and thermal behaviors of the battery cell, capturing key parameters such as voltage, SoC, and temperature. Meanwhile, the aging model is designed to estimate the degradation of the cell over time.

3.2. Description of the Complete Electro-Thermal and Lifetime Model

This paper utilizes a 1D electro-thermal model based on a semi-empirical approach within a MATLAB/Simulink^® R2024b interface. The model aims to replicate the cell’s electrical and thermal performance through two primary components: the electrical and thermal modules. The electrical module calculates the SoC using electrical parameters, while the thermal module estimates the cell’s temperature based on the heat generation equation.

The thermal aspect of the model incorporates thermodynamic equations specific to cylindrical cells. It assumes a single temperature point, where heat is generated at a particular location on the cell’s surface, defined by its specific heat capacity and mass.

The lifetime model is based on neural networks and uses a two-layer feed-forward neural network configuration. The network utilizes 10 hidden neurons, and the dataset is divided, with 75% used for training and 25% for validation and testing. The model was validated using a set of previously unknown inputs and long-term cycling data.

Figures of each model validation and a full description of their methodology are found in [35].

4. ANN-MPC

4.1. Model Predictive Control

Model Predictive Control (MPC) is an advanced control strategy that finds broad applications across fields like engineering, economics, and robotics [22,36]. It uses a system’s mathematical model to predict future behavior and make optimal control decisions. What sets MPC apart from traditional methods is its ability to operate over a predetermined prediction horizon—a future time window during which it forecasts the system’s response to various inputs.

MPC works by formulating an optimization problem that seeks to enhance system performance over the prediction horizon. This is typically achieved by minimizing a cost function, which might involve tracking a reference trajectory or reducing operational costs, all while adhering to system constraints. At every time step, MPC solves this optimization problem using the system’s current state and applies the first control input. Once the control action is implemented, the system’s state is updated, and the optimization process is repeated, offering continuous feedback control. Figure 3 illustrates the flow of MPC and its integration with the semi-empirical model.

In this study, MPC is applied to minimize battery temperature and simultaneously maximize the SoC under a fast-charging profile. The description, development, and validation of the MPC have been previously detailed in [37], and the same approach will be extended to develop a combined MPCANN model in this work.

4.2. Artificial Neural Networks

Artificial Neural Networks (ANNs) have demonstrated high accuracy in battery estimation tasks [30,31,32,33,34]. Among these, feed-forward neural networks (FNNs) stand out as a particularly effective approach for dynamic systems, making them suitable for modeling battery degradation. FNNs excel in predicting a single output, such as capacity degradation, which aligns with the requirements of this study. Therefore, a feed-forward neural network architecture was employed to build the lifetime model. Figure 4 illustrates a typical two-layer FNN configuration, with the corresponding mathematical expressions presented below [38]:

$$y_i=\sigma \left({\displaystyle \sum }_{l=1}^L{\omega }_{ij}\sigma \left({\displaystyle \sum }_{j=1}^L{v}_{lj}{x}_j+v_{lj}\right)+w_{i0}\right) i=1,2,\dots ,m$$

(1)

where V and W represent the weight matrices, while v_i0 and w_j0 denote the firing thresholds. The function σ(.) serves as the mapping function. The inputs to the network are the signals x₁, x₂, …, and x_n, and the outputs are y₁, y₂, …, and y_m. After initializing the network’s weights and biases, it becomes ready for training. The network utilizes 10 hidden neurons, and the dataset is divided, with 75% used for training and 25% for validation and testing. All these processes—training, validation, and testing—are conducted in the MATLAB/Simulink^® R2024b environment to ensure compatibility with the electro-thermal model.

4.3. Concept of ANN-MPC

To reduce the computational complexity and resource demands typically associated with MPC, a combination of an ANN and MPC is proposed. As highlighted earlier, ANNs are highly effective for tasks involving single-output mapping. The concept of the integrated ANN-MPC framework is illustrated in Figure 5.

Conceptually, a neural network (NN) is integrated with an MPC, where the input and output data generated by the MPC serve as the training set for the ANN-MPC. Typically, the neural network is trained offline using the data samples collected from the MPC’s operation. The measurement data produced by the MPC are stored in tables, and to ensure thorough data coverage, a comprehensive training dataset is gathered. Once trained, the ANN-MPC can operate independently, using straightforward mathematical functions to compute complex simulations and optimization algorithms efficiently.

5. Simulation Study

5.1. Description of the Case Study

In this section, the proposed ANN-MPC is validated through a simulation study of a fast-charging profile (Figure 6). This profile initiates with a high charging current of 4C (12 A) until the battery voltage reaches the maximum recommended upper limit of 4.2 V [35]. This is followed by a constant voltage (CV) phase, which continues until the cut-off current decreases to C/20 (0.15 A). In [37], the high-current phase of the fast-charging profile resulted in elevated temperature levels, exceeding the battery’s safe operating limit (>45 °C). To address this, the authors applied MPC to optimize temperature control, maintaining it within a safe threshold (<45 °C) while maximizing the state of charge (SoC), as illustrated in Figure 6. The computational time to obtain the optimized profile was 5 min and 23 s. Therefore, this scenario is used here as a case study for validating the ANN-MPC. The output from the ANN-MPC, especially the computational time, will be compared to that of the original MPC for accuracy.

5.2. Training of the ANN-MPC for the Case-Study

The ANN-MPC approach offers distinct advantages, such as simplified mathematical expressions and strong approximation capabilities, allowing for the efficient collection of extensive training data. The ANN structure replicates that of the lifetime model, utilizing a two-layer architecture with 10 hidden neurons. The dataset is divided with 75% allocated to training and 25% to validation and testing. Additionally, the MPC model developed in the previous section generates the training data used as inputs for the ANN.

To ensure sufficient data coverage, the MPC training set should be broad enough to encompass the entire operating range of the battery. For this purpose, the fast-charging MPC is simulated with the following initial variables:

$$\begin{gathered} T_{cell}=\left[-10,10,25,35,45,60\right] \\ So{C}_{cell}=\left[0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100\right] \\ {I}_{batt}=\left[0, 2, 5, 10, 15, 20,25,30\right] \end{gathered}$$

(2)

Once the data are generated, the ANN is iteratively trained offline with the recorded MPC data. In the following section, the ANN’s outputs will be compared to the virtual MPC results to validate the model’s accuracy.

5.3. Validation of the Case Study

In this section, the MPCANN is validated using the MPC data presented in the previous section. The validation process involves simulations at three temperatures: 25 °C, 0 °C, and 35 °C. The MPCANN architecture demonstrated remarkable efficiency, with each simulation completing in just 5 s. This represents a significant reduction in computational time compared to the original MPC, which required 5 min and 23 s to obtain the optimized profile.

Figure 7 displays the results at ambient temperature. The MPCANN successfully reproduces the current and temperature evolution of the MPC with high accuracy. However, the SoC evolution shows a noticeable deviation from the MPC results. This suggests that a more refined SoC estimation algorithm may need to be integrated into the MPCANN system for improved accuracy.

The simulation results at 35 °C, also shown in Figure 7, demonstrate close alignment between the MPCANN and MPC for temperature and current evolutions. Yet, the SoC evolution again shows discrepancies. This may indicate that the ANN requires a larger dataset or more complex architecture to achieve accurate SoC estimation at higher temperatures.

Figure 7 also presents the simulation results at 0 °C. At this temperature, the MPCANN closely replicates the MPC simulation results across all parameters. This strong performance at low temperatures provides compelling evidence of the MPCANN model’s efficiency and versatility.

In the end, the MPCANN demonstrates promising results in reproducing MPC behavior across various temperatures, particularly excelling in current and temperature predictions. While SoC estimation accuracy requires improvement, especially at higher temperatures, the overall performance of the MPCANN is encouraging. These results highlight the potential of combining Model Predictive Control with Artificial Neural Networks for advanced battery modeling and battery management systems.

5.4. Discussion of the Results

The MPCANN architecture demonstrated remarkable efficiency, with each simulation completing in just 5 s—a 94% reduction in computational time compared to the original MPC’s 5 min and 23 s. This dramatic improvement directly addresses the critical barrier to real-time MPC implementation identified in prior studies, such as adaptive MPC strategies for hybrid electric vehicles that struggle with computational scalability under thermal constraints. By integrating offline-trained ANNs, MPCANN avoids the iterative optimization loops inherent to traditional MPC, aligning with recent advances in hybrid Machine Learning - Model Predictive Control (ML-MPC) frameworks that prioritize computational efficiency without sacrificing predictive accuracy.

While MPCANN’s offline training minimizes runtime overhead, its dependency on pre-collected MPC data limits adaptability to unseen operating conditions—a weakness shared by many hybrid ML-MPC systems. Future work could integrate recursive ANN training or nonlinear autoregressive architectures (e.g., nonlinear autoregressive neural network with external input (NARXNet)) to enhance SoC estimation robustness at high temperatures, building on methodologies proposed for health-aware charging protocols. Additionally, expanding validation to include extreme drive cycles (e.g., aggressive acceleration profiles) would further stress-test the framework’s real-world applicability.

6. Conclusions

In this paper, an Artificial Neural Network-based model predictive control concept (ANN-MPC) is proposed for VTC6 3Ah 18650-type lithium-ion cells to enhance the model’s capabilities and decrease the computational time of MPCs. This advanced approach combines the predictive power of MPC with the adaptive learning capabilities of ANN. The ANN is trained offline with the input and output data of an MPC algorithm. Validation of the MPCANN concept was conducted using MPC results from a previous study, showcasing its effectiveness in optimizing battery temperature and SoC performance. The MPCANN demonstrates promising results with a 94% reduction in computational time compared to the original MPC’s 5 min and 23 s. While SoC estimation accuracy requires improvement, especially at higher temperatures, the overall performance of the MPCANN is encouraging. These results highlight the potential of combining MPCANN to reduce the computational complexity and demand of MPC.

In the end, this study contributes valuable data and modeling techniques to the field of battery research, offering insights that can inform the design and optimization of battery models and battery management systems. Indeed, the innovative MPCANN concept has the potential to revolutionize BMS design by offering a computationally efficient alternative to traditional MPC approaches. This could enable the implementation of advanced control strategies in resource-constrained environments, such as electric vehicles or portable electronics, where computational power is limited. The MPCANN’s ability to optimize battery temperature and SoC performance can lead to improved charging strategies, extended battery life, and enhanced safety in practical applications.

Future work should focus on enhancing the SoC estimation capabilities of the MPCANN, potentially through the integration of more sophisticated algorithms (e.g., NARXnet) or by expanding the training dataset with other cell technologies (solid-state cells or potassium-ion batteries). Additionally, further validation across a wider range of operational temperature conditions (e.g., −10 °C, 45 °C, and 60 °C) could provide valuable insights into the model’s robustness and applicability in diverse scenarios.

The promising results of the MPCANN validation open new avenues for research in adaptive control strategies for battery systems, potentially leading to significant improvements in computational complexity and demands of highly promising control techniques such as MPC.