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Data-driven cooperative optimal output regulation for linear discrete-time multi-agent systems by online distributed adaptive internal model approach

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Science China(Information Sciences) 2023年第7期66卷 30-45页

作者： Kedi XIE Yi JIANG Xiao YU Weiyao LAN Department of Automation Xiamen University Department of Electrical Engineering City University of Hong Kong Key Laboratory of Control and Navigation(Xiamen University) Fujian Province University

In this study, a data-driven learning algorithm was developed to estimate the optimal distributed cooperative control policy, which solves the cooperative optimal output regulation problem for linear discretetime multi-agent systems. Notably, the dynamics of all the agent systems and exo-system is completely unknown. By combining adaptive dynamic programming with an internal model, a model-free off-policy learning method is proposed to estimate the optimal control gain and the distributed adaptive internal model by only accessing the measurable data of multi-agent systems. Moreover, different from the traditional cooperative adaptive controller design method, a distributed internal model is approximated online. Convergence and stability analyses show that the estimate controller generated by the proposed data-driven learning algorithm converges to the optimal distributed controller. Finally, simulation results verify the effectiveness of the proposed method.

关键词： adaptive dynamic programming cooperative control distributed adaptive internal model multi-agent systems optimal output regulation

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Self-organizing neural intelligent control for nonlinear discrete-time systems with particle swarm optimization

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NONLINEAR dynamicS 2025年第1期113卷 583-595页

作者： Ma, Hongyu Wang, Ding Ren, Jin Qiao, Junfei Beijing Univ Technol Sch Informat Sci & Technol Beijing 100124 Peoples R China Beijing Univ Technol Beijing Key Lab Computat Intelligence & Intelligen Beijing 100124 Peoples R China Beijing Univ Technol Beijing Inst Artificial Intelligence Beijing 100124 Peoples R China Beijing Univ Technol Beijing Lab Smart Environm Protect Beijing 100124 Peoples R China

In this paper, the self-organizing heuristic dynamic programming algorithm is established to solve the approximate optimal control issue for affine nonlinear systems. A self-organizing neural network modeling method based on the particle swarm optimization algorithm is introduced to construct the model network. In contrast to the traditional backpropagation neural network, it has stronger adaptive ability and higher modeling precision for a variety of different complex systems, which substantially boosts the efficiency of the method. In addition, the action network and the critic network are constructed to obtain the approximate optimal control strategy and the optimal cost function, respectively. The convergence of the cost function is proved. It also proved that the state estimation errors and the weight vector estimation errors are uniformly ultimately bounded. Several nonlinear complex systems are selected in the experimental simulation to prove the efficiency of the method.

关键词： adaptive dynamic programming Neural networks Nonlinear systems Reinforcement learning Particle swarm optimization

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Enhancing offline reinforcement learning for wastewater treatment via transition filter and prioritized approximation loss

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NEUROCOMPUTING 2025年 636卷

作者： Yang, Ruyue Wang, Ding Li, Menghua Cui, Chengyu Qiao, Junfei Beijing Univ Technol Sch Informat Sci & Technol Beijing Peoples R China Beijing Univ Technol Beijing Key Lab Computat Intelligence & Intelligen Beijing Peoples R China Beijing Univ Technol Beijing Lab Smart Environm Protect Beijing Peoples R China Beijing Univ Technol Beijing Inst Artificial Intelligence Beijing Peoples R China State Grid Corp China State Grid Beijing Chaoyang Power Supply Branch Beijing Peoples R China

Wastewater treatment plays a crucial role in urban society, requiring efficient control strategies to optimize its performance. In this paper, we propose an enhanced offline reinforcement learning (RL) approach for wastewater treatment. Our algorithm improves the learning process. It uses a transition filter to sort out low- performance transitions and employs prioritized approximation loss to achieve prioritized experience replay with uniformly sampled loss. Additionally, the variational autoencoder is introduced to address the problem of distribution shift in offline RL. The proposed approach is evaluated on a nonlinear system and wastewater treatment simulation platform, demonstrating its effectiveness in achieving optimal control. The contributions of this paper include the development of an improved offline RL algorithm for wastewater treatment and the integration of transition filtering and prioritized approximation loss. Evaluation results demonstrate that the proposed algorithm achieves lower tracking error and cost.

关键词： Offline reinforcement learning Wastewater treatment Variational autoencoder adaptive dynamic programming

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dynamic event-driven optimal consensus control for state-constrained multiagent zero-sum differential graphical games

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APPLIED MATHEMATICS AND COMPUTATION 2025年 484卷

作者： Guo, Siyu Pan, Yingnan Li, Hongyi Bohai Univ Coll Control Sci & Engn Jinzhou 121013 Liaoning Peoples R China Southwest Univ Coll Elect & Informat Engn Chongqing 400715 Peoples R China Southwest Univ Chongqing Key Lab Gener Technol & Syst Serv Robots Chongqing 400715 Peoples R China

In this paper, a dynamic event-driven optimal control scheme is proposed for the zero-sum differential graphical games in nonlinear multiagent systems with full-state constraints. Initially, to address the dual demands of optimality and state constraints, a set of system transformation functions are introduced to satisfy the state constraints of the agents. Then, by applying the principle of differential game theory, the distributed optimal control problem affected by external disturbances is formulated as a zero-sum differential graphical game, and the performance index function related to neighbor informations and disturbances is designed for each follower. Afterwards, to enhance the utilization of communication resource, a novel dynamic event- triggered mechanism characterized by a dynamic threshold parameter and an auxiliary dynamic variable is developed, which not only exhibits greater flexibility but also diminishes the frequency of triggers. Furthermore, the approximate optimal control strategies are obtained by employing an event-driven adaptive dynamic programming algorithm. Ultimately, a simulation example is presented to verify the applicability of the proposed control approach.

关键词： adaptive dynamic programming dynamic event-triggered mechanism Full-state constraints Zero-sum differential graphical games

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Finite-time safe reinforcement learning control of multi-player nonzero-sum game for quadcopter systems

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INFORMATION SCIENCES 2025年 712卷

作者： Tan, Junkai Xue, Shuangsi Guan, Qingshu Qu, Kai Cao, Hui Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Peoples R China Xi An Jiao Tong Univ State Key Lab Xian 710049 Peoples R China

This paper investigates a finite-time safe reinforcement learning control algorithm for multi-player nonzero-sum games (FT-SRL-NZS). In addressing the finite-time safe optimal control issue, value functions incorporating designated barrier functions for the involved players are established within the transformed finite-time stable space. The finite-time safe optimal controller is derived from the solution to the transformed Nash equilibrium condition. An actor-critic structure is proposed for solving the Hamilton-Jacobi-Bellman (HJB) equation in the finite-time stable space, aimed at approximating the finite-time optimal value and its corresponded controller using a novel finite-time concurrent learning update law. A dynamic event-trigger rule adjusts the trigger condition in real time, thereby minimizing the computational and communicative demands associated with calculating Nash equilibrium. Lyapunov stability analysis is employed to examine the finite-time equilibrium of the closed-loop system. Numerical simulations and unmanned aerial vehicle (UAV) hardware tests are carried out to illustrate the efficacy of the proposed finite-time safe control algorithm.

关键词： Finite-time optimal control Nonzero-sum game Reinforcement learning Neural network dynamic event-trigger adaptive dynamic programming

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Relaxed Optimal Control With Self-Learning Horizon for Discrete-Time Stochastic dynamics

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IEEE TRANSACTIONS ON CYBERNETICS 2025年第3期55卷 1183-1196页

作者： Wang, Ding Wang, Jiangyu Liu, Ao Liu, Derong Qiao, Junfei Beijing Univ Technol Sch Informat Sci & Technol Beijing Key Lab Computat Intelligence & Intelligen Beijing Lab Smart Environm Protect Beijing 100124 Peoples R China Beijing Univ Technol Beijing Inst Artificial Intelligence Beijing 100124 Peoples R China Southern Univ Sci & Technol Sch Automat & Intelligent Mfg Shenzhen 518055 Peoples R China Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA

The innovation of optimal learning control methods is profoundly propelled due to the improvement of the learning ability. In this article, we investigate the synthesis of initialization and acceleration for optimal learning control algorithms. This approach contrasts with traditional methods that concentrate solely on either the improvement of initialization or acceleration. Specifically, we establish a novel relaxed policy iteration (PI) algorithm with self-learning horizon for stochastic optimal control. Notably, by suitably utilizing self-learning horizon, we can directly evaluate inadmissible policies to reduce the initialization burden. Meanwhile, the inadmissible policy can be rapidly optimized with few learning iterations. Then, several critical conclusions of relaxed optimal control are established by discussing algorithm convergence and system stability. Furthermore, to provide the convincing application potentials, a class of unconventional problems is effectively solved by the relaxed PI algorithm, including the dynamics with external noises and nonzero equilibrium. Finally, we present a series of nonlinear benchmarks with practical applications to comprehensively evaluate the performance of relaxed PI. The experimental results obtained from these diverse benchmarks uniformly highlight the effectiveness of self-learning horizon mechanism.

关键词： Optimal control Heuristic algorithms Cost function Costs Convergence Noise Stability criteria dynamic programming Cybernetics Benchmark testing adaptive dynamic programming external noises nonzero equilibrium optimal control policy iteration (PI) relaxed optimal control stability in probability stochastic dynamics

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Data-based neural controls for an unknown continuous-time multi-input system with integral reinforcement

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Control Theory and Technology 2025年第1期23卷 118-130页

作者： Yongfeng Lv Jun Zhao Wan Zhang Huimin Chang College of Electrical and Power Engineering Taiyuan University of TechnologyTaiyuanShanxi030024China College of Transportation Shandong University of Science and TechnologyQingdao266590ShandongChina School of Mathematical Sciences Shanxi UniversityTaiyuan030006ShanxiChina

Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time ***,solving the Hamilton-Jacobi-Bellman(HJB)equations for nonlinear systems requires precise and complicated ***,the research and application of IRL in continuous-time(CT)systems must be further *** develop the IRL of a CT nonlinear system,a data-based adaptive neural dynamic programming(ANDP)method is proposed to investigate the optimal control problem of uncertain CT multi-input systems such that the knowledge of the dynamics in the HJB equation is ***,the multi-input model is approximated using a neural network(NN),which can be utilized to design an integral reinforcement ***,two criterion networks and one action network are constructed based on the integral reinforcement signal.A nonzero-sum Nash equilibrium can be reached by learning the optimal strategies of the multi-input *** this scheme,the NN weights are constantly updated using an adaptive *** weight convergence and the system stability are analyzed in *** optimal control problem of a multi-input nonlinear CT system is effectively solved using the ANDP scheme,and the results are verified by a simulation study.

关键词： adaptive dynamic programming Integral reinforcement Neural networks Heuristic dynamic programming Multi-input system

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Privacy-preserving ADP for secure tracking control of AVRs against unreliable communication

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FRONTIERS IN NEUROROBOTICS 2025年 19卷 1549414页

作者： Zhang, Kun Han, Kezhen Hu, Zhijian Tan, Guoqiang Beihang Univ Sch Astronaut Beijing Peoples R China Univ Jinan Sch Elect Engn Jinan Peoples R China Univ Toulouse LAAS CNRS Toulouse France Loughborough Univ Dept Aeronaut & Automot Engn Loughborough England

In this study, we developed an encrypted guaranteed-cost tracking control scheme for autonomous vehicles or robots (AVRs), by using the adaptive dynamic programming technique. To construct the tracking dynamics under unreliable communication, the AVR's motion is analyzed. To mitigate information leakage and unauthorized access in vehicular network systems, an encrypted guaranteed-cost policy iteration algorithm is developed, incorporating encryption and decryption schemes between the vehicle and the cloud based on the tracking dynamics. Building on a simplified single-network framework, the Hamilton-Jacobi-Bellman equation is approximately solved, avoiding the complexity of dual-network structures and reducing the computational costs. The input-constrained issue is successfully handled using a non-quadratic value function. Furthermore, the approximate optimal control is verified to stabilize the tracking system. A case study involving an AVR system validates the effectiveness and practicality of the proposed algorithm.

关键词： adaptive dynamic programming encryption and decryption tracking control optimal control autonomous vehicle

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Distributed data-driven three-dimensional optimal formation control for underactuated AUVs with actuator saturation and unknown dynamics

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OCEAN ENGINEERING 2025年 325卷

作者： Gong, Huibin Er, Meng Joo Liu, Yi Fan, Gaofeng Dalian Maritime Univ Inst Artificial Intelligence & Marine Robot Coll Marine Elect Engn Dalian 116026 Peoples R China

The optimality of formation control for underactuated autonomous underwater vehicles (AUVs) is a topic of interest. Towards this end, a leader-follower-based distributed data-driven optimal formation control scheme is proposed to address three-dimensional (3-D) optimal formation control of underactuated AUVs with actuator saturation, completely unknown dynamics, and environmental disturbances. The proposed scheme has the following features: (1) Underactuation and actuator saturation problems are handled by transforming coordinates and designing an asymmetric smooth saturation model, respectively. (2) A radial basis function neural network (RBFNN)-based data-driven model is established to reconstruct unknown dynamics through input and output data. (3) The transformation of an error dynamic system with an affine form and anti- saturation control design are implemented via backstepping and an adaptive law. (4) An adaptive dynamic programming optimal controller with a single critic network is established using a RBFNN to optimize formation errors and control energy while ensuring system stability. An improved weight update law is designed to relax initial stabilization control requirements. After theoretical analysis, the proposed scheme can enable all signals in the closed-loop system to be bounded, and formation errors can converge to arbitrarily small intervals. The effectiveness and advantages of the proposed scheme are proved by simulation studies.

关键词： Underactuated autonomous underwater vehicles Distributed optimal control Unknown dynamics Actuator saturation adaptive dynamic programming Neural networks

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dynamic Event-Driven ADP for N-Player Nonzero-Sum Games of Constrained Nonlinear Systems

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 7657-7669页

作者： Guo, Siyu Pan, Yingnan Li, Hongyi Cao, Liang Bohai Univ Coll Control Sci & Engn Jinzhou 121013 Liaoning Peoples R China Southwest Univ Coll Elect & Informat Engn Chongqing 400715 Peoples R China Bohai Univ Coll Math Sci Jinzhou 121013 Liaoning Peoples R China

In this paper, the dynamic event-driven optimal control problem is investigated for a class of continuous-time nonlinear systems subject to asymmetric input constraints in the framework of nonzero-sum (NZS) games. Initially, by constructing a modified value function, the respective asymmetric input constraint requirements of the controllers involved in the NZS games are successfully satisfied. Then, based on the Bellman's optimality principle, the N-coupled Hamilton-Jacobi equations are derived for the N-player NZS games. After that, the adaptive dynamic programming (ADP) method is employed to seek for the optimal control policies, in which the simpler single critic neural network structure, instead of the dual network structure of actor-critic in the typical ADP algorithm, is applied. Furthermore, an improved critic network weight updating law is proposed to ensure the stability of the closed-loop system without a hard-to-find initial admissible control scheme. In addition, in order to reduce the update frequency of the controllers to a greater extent, a dynamic event-driven mechanism with adjustable threshold is developed. Finally, a simulation example is given to demonstrate the validity of the developed event-driven control scheme. Note to Practitioners-This paper aims to address the NZS games problem for a category of multi-player continuous-time nonlinear systems featuring multiple input constraints. The applicability of this approach can be widely extended to practical domains, including control applications for reconfigurable robot systems, networked communication systems, etc. The majority of researches on multi-player NZS games problem are focused on the impact of symmetric input constraints. Especially under the premise of ensuring controller optimality, the challenge lies in how to ensure effective control functionality while subjecting the controller to asymmetric constraints. Furthermore, the existing ADP algorithms often depend on an initial admissibl

关键词： Games Optimal control Heuristic algorithms Nonlinear dynamical systems Nash equilibrium dynamic programming Differential games Aerodynamics Process control Power system stability adaptive dynamic programming asymmetric input constraints dynamic event-driven mechanism nonzero-sum games

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