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17 pages, 1314 KiB

Open AccessFeature PaperArticle

Distributed Optimization Control for the System with Second-Order Dynamic

by Yueqing Wang, Hao Zhang and Zhi Li

Mathematics 2024, 12(21), 3347; https://doi.org/10.3390/math12213347 - 25 Oct 2024

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No matter whether with constraint or without constraint, most of the research about distributed optimization is studied for the kind of quadratic performance criteria that does not have an integrator; these optimization problems only concern the state value at the time of the [...] Read more.

No matter whether with constraint or without constraint, most of the research about distributed optimization is studied for the kind of quadratic performance criteria that does not have an integrator; these optimization problems only concern the state value at the time of the final state, not the whole process of the system change. For this problem, this paper discusses second-order multi-agent systems with a discrete-time dynamic and a continuous-time dynamic, respectively, for distributed optimization control problems, and proposes sufficient conditions to ensure the quadratic performance criteria with an integrator is positive. Specifically, under sufficient conditions, we describe the multi-agent systems that are considered in this paper to be connected topology; all the agents can obtain the information from their neighbors. In addition, the structure of our controller only relies on the Laplace matrix of the system’s topology, and the reaction coefficients in the controller are the parameters in the performance criteria. Finally, the analysis of convergence is given and verified by numerical examples and simulations. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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24 pages, 2214 KiB

Open AccessArticle

Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization

by Junming Chen, Kai Zhang, Hui Zeng, Jin Yan, Jin Dai and Zhidong Dai

Mathematics 2024, 12(19), 3075; https://doi.org/10.3390/math12193075 - 30 Sep 2024

Viewed by 669

Abstract

The key problem to solving constrained multi-objective optimization problems (CMOPs) is how to achieve a balance between objectives and constraints. Unfortunately, most existing methods for CMOPs still cannot achieve the above balance. To this end, this paper proposes an adaptive constraint relaxation-based evolutionary [...] Read more.

The key problem to solving constrained multi-objective optimization problems (CMOPs) is how to achieve a balance between objectives and constraints. Unfortunately, most existing methods for CMOPs still cannot achieve the above balance. To this end, this paper proposes an adaptive constraint relaxation-based evolutionary algorithm (ACREA) for CMOPs. ACREA adaptively relaxes the constraints according to the iteration information of population, whose purpose is to induce infeasible solutions to transform into feasible ones and thus improve the ability to explore the unknown regions. Completely ignoring constraints can cause the population to waste significant resources searching for infeasible solutions, while excessively satisfying constraints can trap the population in local optima. Therefore, balancing constraints and objectives is a crucial approach to improving algorithm performance. By appropriately relaxing the constraints, it induces infeasible solutions to be transformed into feasible ones, thus obtaining more information from infeasible solutions. At the same time, it also establishes an archive for the storage and update of solutions. In the archive update process, a diversity-based ranking is proposed to improve the convergence speed of the algorithm. In the selection process of the mating pool, common density selection metrics are incorporated to enable the algorithm to obtain higher-quality solutions. The experimental results show that the proposed ACREA algorithm not only achieved the best Inverse Generation Distance (IGD) value in 54.6% of the 44 benchmark test problems and the best Hyper Volume (HV) value in 50% of them, but also obtained the best results in seven out of nine real-world problems. Clearly, CP-TSEA outperforms its competitors. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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18 pages, 1077 KiB

Open AccessArticle

Reinforcement Learning with Value Function Decomposition for Hierarchical Multi-Agent Consensus Control

by Xiaoxia Zhu

Mathematics 2024, 12(19), 3062; https://doi.org/10.3390/math12193062 - 30 Sep 2024

Viewed by 620

Abstract

A hierarchical consensus control algorithm based on value function decomposition is proposed for hierarchical multi-agent systems. To implement the consensus control algorithm, the reward function of the multi-agent systems can be decomposed, and two value functions can be obtained by analyzing the communication [...] Read more.

A hierarchical consensus control algorithm based on value function decomposition is proposed for hierarchical multi-agent systems. To implement the consensus control algorithm, the reward function of the multi-agent systems can be decomposed, and two value functions can be obtained by analyzing the communication content and the corresponding control objective of each layer in the hierarchical multi-agent systems. Therefore, for each agent in the systems, a dual-critic network and a single-actor network structure are applied to realize the objective of each layer. In addition, the target network is introduced to prevent overfitting in the critic network and improve the stability of the online learning process. During the updating of network parameters, a soft updating mechanism and experience replay buffer are introduced to slow down the update rate of the network and improve the utilization rate of training data. The convergence and stability of the consensus control algorithm with the soft updating mechanism are analyzed theoretically. Finally, the correctness of the theoretical analysis and the effectiveness of the algorithm were verified by two experiments. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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16 pages, 3484 KiB

Open AccessArticle

A Fixed-Time Event-Triggered Consensus of a Class of Multi-Agent Systems with Disturbed and Non-Linear Dynamics

by Yueqing Wang, Te Wang and Zhi Li

Mathematics 2024, 12(19), 3009; https://doi.org/10.3390/math12193009 - 26 Sep 2024

Viewed by 444

Abstract

This paper investigates the problem of fixed-time event-triggered consensus control for a class of multi-agent systems with disturbed and non-linear dynamics. A fixed-time consensus protocol based on an event-triggered strategy is proposed, which can ensure a fixed-time event-triggered consensus, reduce energy consumption, and [...] Read more.

This paper investigates the problem of fixed-time event-triggered consensus control for a class of multi-agent systems with disturbed and non-linear dynamics. A fixed-time consensus protocol based on an event-triggered strategy is proposed, which can ensure a fixed-time event-triggered consensus, reduce energy consumption, and decrease the frequency of controller updates. The control protocol can also be applied to the case when the systems are free of disturbances; it solves the problem of high convergence time of the systems and reduces energy consumption of the systems. Sufficient conditions are proposed for the multi-agent systems with disturbed and non-linear dynamics to achieve the fixed-time event-triggered consensus by using algebraic graph theory, inequalities, fixed-time stability theory, and Lyapunov stability theory. Finally, simulation results show that the proposed control protocol has the advantages of both event-triggered and fixed-time convergence; compared to previous work, the convergence time of the new control protocol is greatly reduced (about 1.5 s) and the update times are also greatly reduced (less than 50 times), which is consistent with the theoretical results. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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24 pages, 513 KiB

Open AccessArticle

The Impact of Digital Economy on TFP of Industries: Empirical Analysis Based on the Extension of Schumpeterian Model to Complex Economic Systems

by Jiaqi Liu, Yiyang Cheng, Yamei Fu and Fei Xue

Mathematics 2024, 12(17), 2619; https://doi.org/10.3390/math12172619 - 23 Aug 2024

Viewed by 837

Abstract

The digital economy (DE) is a new driver for enhancing total factor productivity (TFP). Using panel data from 30 provinces in China between 2011 and 2022, this study measures DE and TFP using the entropy-weighted TOPSIS method and the Global Malmquist–Luenberger method and [...] Read more.

The digital economy (DE) is a new driver for enhancing total factor productivity (TFP). Using panel data from 30 provinces in China between 2011 and 2022, this study measures DE and TFP using the entropy-weighted TOPSIS method and the Global Malmquist–Luenberger method and further examines the impact of DE on the TFP of industries. The main findings are as follows: (1) DE can significantly improve TFP, though the extent of improvement varies. DE has the greatest impact on the TFP of the service industry, followed by the manufacturing industry, with the weakest effect on the agricultural industry. (2) The enhancement effect of DE on agriculture and the service industry is more pronounced in the central and western regions, while the improvement effect on manufacturing is more evident in the eastern region. (3) DE has facilitated the improvement of TFP in manufacturing industries such as textiles and special equipment manufacturing, as well as in service industries like wholesale and retail. However, it has not had a significant impact on the TFP of industries such as pharmaceutical manufacturing and real estate. This study has significant theoretical value and policy implications for China and other developing countries in exploring DE and achieving high-quality industrial development. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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22 pages, 2800 KiB

Open AccessArticle

Polynomial Iterative Learning Control (ILC) Tracking Control Design for Uncertain Repetitive Continuous-Time Linear Systems Applied to an Active Suspension of a Car Seat

by Selma Ben Attia, Sultan Alzahrani, Saad Alhuwaimel, Salah Salhi and Houssem Eddine Ouerfelli

Mathematics 2024, 12(16), 2573; https://doi.org/10.3390/math12162573 - 20 Aug 2024

Cited by 1 | Viewed by 599

Abstract

This paper addresses the issue of polynomial iterative learning tracking control (Poly-ILC) for continuous-time linear systems (LTI) operating repetitively. It explores the design of an iterative learning control law by examining the stability along the pass theory of 2D repetitive systems. The obtained [...] Read more.

This paper addresses the issue of polynomial iterative learning tracking control (Poly-ILC) for continuous-time linear systems (LTI) operating repetitively. It explores the design of an iterative learning control law by examining the stability along the pass theory of 2D repetitive systems. The obtained result is a generalization of the notion of stability along passages, taking into account transient performances. To strike a balance between stability along passages and transient performance, we extend our developed result in the discrete case, relying on some numerical tools. Specifically, in this work we investigate the convergence of tracking error with given learning controller gains. The key contribution of this structure of control lies in establishing an LMI (linear matrix inequality) condition that ensures both pole placement according to desired specifications and the convergence of output error between iterations. Furthermore, new sufficient conditions for stability regions along the pass addressing the tracking problem of differential linear repetitive processes are developed. Numerical results are provided to demonstrate the effectiveness of the proposed approaches. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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16 pages, 1091 KiB

Open AccessArticle

Adaptive Iterative Learning Tracking Control for Nonlinear Teleoperators with Input Saturation

by Bochun Wu, Xinhao Chen, Jinshan Huang, Jiawen Wen, Jiakun Liu, Fujie Wang and Jianing Zhang

Mathematics 2024, 12(15), 2384; https://doi.org/10.3390/math12152384 - 31 Jul 2024

Viewed by 707

Abstract

Addressing input saturation, external disturbances, and uncertain system parameters, this paper investigates the position tracking control problem for bilateral teleoperation systems with a time delay communication channel. Based on a composite energy function, we propose an adaptive iterative learning control (AILC) method to [...] Read more.

Addressing input saturation, external disturbances, and uncertain system parameters, this paper investigates the position tracking control problem for bilateral teleoperation systems with a time delay communication channel. Based on a composite energy function, we propose an adaptive iterative learning control (AILC) method to achieve the objective of position tracking under the alignment condition. This extends the existing research on the control of nonlinear teleoperation systems with time delay. The saturation constraint property of the Softsign function ensures that no state of the system exceeds its constraints. The controller learns to simultaneously deal with the uncertainty of system parameters online, reject external disturbances, and eliminate positional errors along the time and iteration axes. All signals in the system for any constant time delay are proved to be bounded. Ultimately, the performance of the proposed controller is further verified through numerical simulations. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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11 pages, 654 KiB

Open AccessArticle

Robust Constrained Cooperative Control for Multiple Trains

by Qijie Hu, Xinyu Fan and Yue Wei

Mathematics 2024, 12(13), 2003; https://doi.org/10.3390/math12132003 - 28 Jun 2024

Viewed by 625

Abstract

This paper investigates robust constrained cooperative control for multiple trains, taking into account disturbances, velocity and control input constraints, and nonlinear operation resistances. A robust constrained cooperative control algorithm is employed, utilizing position information from neighboring trains to ensure each train operates within [...] Read more.

This paper investigates robust constrained cooperative control for multiple trains, taking into account disturbances, velocity and control input constraints, and nonlinear operation resistances. A robust constrained cooperative control algorithm is employed, utilizing position information from neighboring trains to ensure each train operates within the desired formation. The effects of external disturbances are examined through multiple transformations and the convexity of stochastic matrices, resulting in an error bound for the final relative positions. This error boundary is correlated with the parameters of the system matrix, initial state conditions, and disturbance amplitudes. The theoretical findings are substantiated with a numerical example. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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17 pages, 4881 KiB

Open AccessArticle

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

by Lijuan Chen, Mingchu Yu, Jinnan Luo, Jinpeng Mi, Kaibo Shi and Song Tang

Mathematics 2024, 12(12), 1891; https://doi.org/10.3390/math12121891 - 18 Jun 2024

Viewed by 652

Abstract

Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. [...] Read more.

Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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18 pages, 2563 KiB

Open AccessArticle

Neural Network-Based Distributed Consensus Tracking Control for Nonlinear Multi-Agent Systems with Mismatched and Matched Disturbances

by Linxi Xu and Kaiyu Qin

Mathematics 2024, 12(9), 1319; https://doi.org/10.3390/math12091319 - 26 Apr 2024

Viewed by 920

Abstract

In practice, disturbances, including model uncertainties and unknown external disturbances, are always widely present and have a significant impact on the cooperative control performance of a networked multi-agent system. In this work, the distributed consensus tracking control problem for a class of multi-agent [...] Read more.

In practice, disturbances, including model uncertainties and unknown external disturbances, are always widely present and have a significant impact on the cooperative control performance of a networked multi-agent system. In this work, the distributed consensus tracking control problem for a class of multi-agent systems subject to matched and mismatched uncertainties is addressed. In particular, the dynamics of the leader agent are modeled with uncertain terms, i.e., the leader’s higher-order information, such as velocity and acceleration, is unknown to all followers. To solve this problem, a robust consensus tracking control scheme that combines a neural network-based distributed observer, a barrier function-based disturbance observer, and a tracking controller based on the back-stepping method was developed in this study. Firstly, a neural network-based distributed observer is designed, which is able to achieve effective estimation of leader information by all followers. Secondly, a tracking controller was designed utilizing the back-stepping technique, and the boundedness of the closed-loop error system was proved using the Lyapunov-like theorem, which enables the followers to effectively track the leader’s trajectory. Meanwhile, a barrier function-based disturbance observer is proposed, which achieves the effective estimation of matched and mismatched uncertainties of followers. Finally, the effectiveness of the robust consensus tracking control method designed in this study was verified through numerical simulations. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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16 pages, 1832 KiB

Open AccessArticle

Multi-Objective Optimization of Cell Voltage Based on a Comprehensive Index Evaluation Model in the Aluminum Electrolysis Process

by Chenhua Xu, Wenjie Zhang, Dan Liu, Jian Cen, Jianbin Xiong and Guojuan Luo

Mathematics 2024, 12(8), 1174; https://doi.org/10.3390/math12081174 - 14 Apr 2024

Cited by 1 | Viewed by 1207

Abstract

In the abnormal situation of an aluminum electrolysis cell, the setting of cell voltage is mainly based on manual experience. To obtain a smaller cell voltage and optimize the operating parameters, a multi-objective optimization method for cell voltage based on a comprehensive index [...] Read more.

In the abnormal situation of an aluminum electrolysis cell, the setting of cell voltage is mainly based on manual experience. To obtain a smaller cell voltage and optimize the operating parameters, a multi-objective optimization method for cell voltage based on a comprehensive index evaluation model is proposed. Firstly, a comprehensive judgment model of the cell state based on the energy balance, material balance, and stability of the aluminum electrolysis process is established. Secondly, a fuzzy neural network (FNN) based on the autoregressive moving average (ARMA) model is designed to establish the cell-state prediction model in order to finish the real-time monitoring of the process. Thirdly, the optimization goal of the process is summarized as having been met when the difference between the average cell voltage and the target value reaches the minimum, and the condition of the cell is excellent. And then, the optimization setting model of cell voltage is established under the constraints of the production and operation requirements. Finally, a multi-objective antlion optimization algorithm (MOALO) is used to solve the above model and find a group of optimized values of the electrolysis cell, which is used to realize the optimization control of the cell state. By using actual production data, the above method is validated to be effective. Moreover, optimized operating parameters are used to verify the prediction model of cell voltage, and the cell state is just excellent. The method is also applied to realize the optimization control of the process. It is of guiding significance for stabilizing the electrolytic aluminum production and achieving energy saving and consumption reduction. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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29 pages, 6845 KiB

Open AccessArticle

Research on Improved Differential Evolution Particle Swarm Hybrid Optimization Method and Its Application in Camera Calibration

by Xinyu Sha, Fucai Qian and Hongli He

Mathematics 2024, 12(6), 870; https://doi.org/10.3390/math12060870 - 15 Mar 2024

Viewed by 943

Abstract

The calibration of cameras plays a critical role in close-range photogrammetry because the precision of calibration has a direct effect on the quality of results. When handling image capture using a camera, traditional swarm intelligence algorithms such as genetic algorithms and particle swarm [...] Read more.

The calibration of cameras plays a critical role in close-range photogrammetry because the precision of calibration has a direct effect on the quality of results. When handling image capture using a camera, traditional swarm intelligence algorithms such as genetic algorithms and particle swarm optimization, in conjunction with Zhang’s calibration method, frequently face difficulties regarding local optima and sluggish convergence. This study presents an enhanced hybrid optimization approach utilizing both the principles of differential evolution and particle swarm optimization, which is then employed in the context of camera calibration. Initially, we establish a measurement model specific to the camera in close-range photogrammetry and determine its interior orientation parameters. Subsequently, employing these parameters as initial values, we perform global optimization and iteration using the improved hybrid optimization algorithm. The effectiveness of the proposed approach is subsequently validated through simulation and comparative experiments. Compared to alternative approaches, the proposed algorithm enhances both the accuracy of camera calibration and the convergence speed. It effectively addresses the issue of other algorithms getting trapped in local optima due to image distortion. These research findings provide theoretical support for practical engineering applications in the field of control theory and optimization to a certain extent. Full article

(This article belongs to the Special Issue Advance in Control Theory and Optimization)

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