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Barrier-critic-disturbance approximate optimal control of nonzero-sum differential games for modular robot manipulators

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NEURAL NETWORKS 2025年 181卷 106880页

作者： Dong, Bo Zhu, Xinye An, Tianjiao Jiang, Hucheng Ma, Bing Changchun Univ Technol Dept Control Sci & Engn Changchun 130012 Jilin Peoples R China

In this paper, for addressing the safe control problem of modular robot manipulators (MRMs) system with uncertain disturbances, an approximate optimal control scheme of nonzero-sum (NZS) differential games is proposed based on the control barrier function (CBF). The dynamic model of the manipulator system integrates joint subsystems through the utilization of joint torque feedback (JTF) technique, incorporating interconnected dynamic coupling (IDC) effects. By integrating the cost functions relevant to each player with the CBF, the evolution of system states is ensured to remain within the safe region. Subsequently, the optimal tracking control problem for the MRM system is reformulated as an NZS game involving multiple joint subsystems. Based on the adaptive dynamic programming (ADP) algorithm, a cost function approximator for solving Hamilton-Jacobi (HJ) equation using only critic neural networks (NN) is established, which promotes the feasible derivation of the approximate optimal control strategy. The Lyapunov theory is utilized to demonstrate that the tracking error is uniformly ultimately bounded (UUB). Utilizing the CBF's state constraint mechanism prevents the robot from deviating from the safe region, and the application of the NZS game approach ensures that the subsystems of the MRM reach a Nash equilibrium. The proposed control method effectively addresses the problem of safe and approximate optimal control of MRM system under uncertain disturbances. Finally, the effectiveness and superiority of the proposed method are verified through simulations and experiments.

关键词： adaptive dynamic programming Control barrier function Nonzero-sum game Modular robot manipulator Optimal control

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Robust Optimal Consensus Control for Nonlinear Multi-agent Systems: Two Hybrid dynamic Event-Triggered-Based Approach

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INTERNATIONAL JOURNAL OF adaptive CONTROL AND SIGNAL PROCESSING 2025年第2期39卷 398-423页

作者： Zou, Haoming Zhang, Guoshan Tianjin Univ Sch Elect & Informat Engn Tianjin Peoples R China

In this paper, the dynamic event-triggered robust optimal consensus control problem is investigated for nonlinear multi-agent systems (MASs) with matched and mismatched disturbances via integral sliding mode (ISM) control and the adaptive dynamic programming (ADP) algorithm. First, a dynamic event-triggered fixed-time ISM controller is designed to guarantee that the system state converges to the predefined ISM manifold, thereby eliminating the matched disturbances. Next, the consensus control problem is transformed into an optimal control problem by constructing neighborhood error dynamics and a new modified cost function;thus, an event-triggered-based coupled Hamilton-Jacobi-Bellman equation (HJBE) is established. Then, an ADP-based single-critic neural network (NN) is constructed to solve coupled HJBE to obtain the event-triggered optimal controller, in which the NN weight is updated only at the triggering instants. Through the implementation of these two dynamic event-triggered mechanisms, resources and controller execution time can be saved. It is proved that the whole closed-loop system signals are uniformly ultimately bounded by the Lyapunov technique. Finally, two illustrative examples verify the effectiveness and superiority of the proposed control scheme.

关键词： adaptive dynamic programming dynamic event-triggered mechanisms integral sliding mode control robust consensus control

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Event-triggered H∞ control for unknown constrained nonlinear systems with application to robot arm

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APPLIED MATHEMATICAL MODELLING 2025年 144卷

作者： Qin, Chunbin Jiang, Kaijun Wang, Yuchen Zhu, Tianzeng Wu, Yinliang Zhang, Dehua Henan Univ Sch Artificial Intelligence Zhengzhou 450000 Peoples R China

In this paper, an event-triggered safe H-infinity, control approach is investigated for nonlinear continuous-time systems with asymmetric constrained-input and state constraints. The proposed method is based on adaptive dynamic programming and addresses systems with completely unknown dynamics. Firstly, the unknown dynamics is identified using three neural networks. Secondly, a novel nonquadratic type function is introduced to address the asymmetric constrained- input. Next, the intention behind integrating the value function with the control barrier function is to guide the system state to evolve within the safe area. This also leads to a novel safe Hamilton-Jacobi-Isaacs equation. Next, the event-triggered condition is established with a designated threshold, ensuring the system stability. Unlike the classical actor-critic neural network approach, we only require a critic neural network to estimate the safe Hamilton-Jacobi-Isaacs equation, thereby achieving online solution under state constraints. Utilizing the Lyapunov stability approach and considering the joint impact of asymmetric constrained-input and state constraints, the system state and critic neural network weights exhibit uniformly ultimately bounded, effectively eliminating Zeno behavior. In conclusion, the efficacy of the proposed scheme is demonstrated through a simulation example involving a robot arm system.

关键词： Asymmetric constrained-input adaptive dynamic programming H-infinity control Safety Event-triggered control Robot arm system

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Temporal difference learning with multi-step returns for intelligent optimal control of dynamic systems☆

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NEUROCOMPUTING 2025年 622卷

作者： Xin, Peng Wang, Ding Liu, Ao 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 article, the adaptive neural control algorithm based on the A-return mechanism [ANC(A)] is developed under the temporal difference learning framework to address the optimal control problems of complex dynamic systems. First, in the light of the classical value iteration (VI) framework, a novel iteration mechanism is established, including the general value function, control policy, and the multi-step return value function, where the multi-step value function is constructed through multi-step returns and temporal difference with long-term prediction factor A [TD(A)]. Meanwhile, the generalized VI idea is incorporated into the specific implementation process of the ANC(A) algorithm. The general iterative value function and the A-return iterative value function are respectively initialized from zero and a larger positive definite function. Subsequently, the convergence of the ANC(A) algorithm is rigorously analyzed, that is, the general iterative value function and the A-return iterative value function converge to the optimal value in a monotonically increasing and monotonically decreasing manner, respectively. Finally, the effectiveness and progressiveness of the ANC(A) algorithm are demonstrated by conducting the power system application and the nonlinear system simulation.

关键词： adaptive dynamic programming Convergence Optimal control Reinforcement learning Temporal difference

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adaptive prescribed performance optimal control for strict-feedback nonlinear systems with input delay and input quantization

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JOURNAL OF THE FRANKLIN INSTITUTE 2025年第4期362卷

作者： Xia, Xiaonan Li, Chun Zhang, Tianping Fang, Yu Yangzhou Univ Coll Informat Engn Dept Automat Yangzhou 225127 Peoples R China

In this paper, an adaptive optimal control strategy is proposed based on command filter technique for a class of strict-feedback nonlinear systems with input quantization and input delay, as well as prescribed performance. Utilizing dynamic surface control (DSC) and an error compensation mechanism, the impact of filtering errors on system performance is eliminated, and the difficulties of optimal control caused by input delay and input quantization are overcome. Based on identifier-critic-actor optimal architecture and by introducing positive definite functions with the application of gradient descent approach, the persistence excitation condition is relaxed. Through the cost function with prescribe performance and the compensation method in virtual control and adaptive law design, the system prescribed performance is achieved. The control scheme not only ensures that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), but also minimizes the cost function and saves network resources. Finally, the simulation example is given to verify the effectiveness of the algorithm.

关键词： Uncertain nonlinear systems adaptive dynamic programming Optimal control Input quantization and input delay Prescribed performance

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Attack-Defense Game of Heterogeneous Multi-Agent Systems Under Actuator Faults

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 14699-14711页

作者： Li, Yadong Hu, Bin Li, Tao Guan, Zhi-Hong Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan 430074 Peoples R China South China Univ Technol Sch Future Technol Guangzhou 510006 Peoples R China Guangdong Artificial Intelligence & Digital Econ L Guangzhou 510006 Peoples R China Hubei Normal Univ Sch Elect Engn & Automat Huangshi 435002 Peoples R China

This paper investigates N versus N attack-defense game problem of heterogeneous nonlinear multi-agent systems under the condition of actuator faults on the defensive side. Specifically, N attackers need to approach the target area as closely as possible in order to attack it, while N defenders need to approach the attackers as closely as possible and intercept them. We decompose this problem into two N-player nonzero-sum game problems. Based on differential game method, the optimal attacking game strategies for the attackers are first presented. Then, considering that the defenders contains actuator faults, this paper designs a fault observer for each defending agent based on adaptive estimation theory to estimate unknown actuator fault and proposes a novel optimal defense game strategy applicable for actuator fault. To address the problem that it is difficult to directly solve the optimal control strategies in nonlinear systems, we propose an online learning algorithm based on adaptive dynamic programming to obtain approximate solutions for the optimal cost functions and the optimal control strategies. The effectiveness of the proposed method is verified through theoretical analysis and simulation examples. Note to Practitioners-The problem of attack-defense confrontation for multi-agent systems has a broad practical background, such as resource competition, missile interception, and base defense, etc. By introducing game theory, complex attack-defense confrontation problems for multi-agent systems can be clearly formulated. However, most studies on attack-defense game confrontation are still limited to a small number of intelligent agents. Additionally, actuator faults with frequent and great harm pose significant challenges to the safe and stable operation of multi-agent systems in complex and changeable practical applications. Especially in the attack-defense confrontation scenario, actuator faults may be caused not only by the system's own physical faults but a

关键词： Games Actuators Multi-agent systems Differential games Missiles Optimal control Intelligent agents Automation Artificial intelligence Training Heterogeneous multi-agent systems actuator faults attack-defense game differential game adaptive dynamic programming

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adaptive Fuzzy Event-Triggered Optimized Consensus Control for Delayed Unknown Stochastic Nonlinear Multi-Agent Systems Using Simplified ADP

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 11780-11793页

作者： Zhang, Guoping Liang, Chengbin Zhu, Quanxin Guizhou Univ Sch Math & Stat Guiyang 550025 Guizhou Peoples R China Guizhou Univ Coll Elect Engn Guiyang 550025 Guizhou Peoples R China Hunan Normal Univ Sch Math & Stat Changsha 410081 Hunan Peoples R China

This paper investigates the adaptive fuzzy event-triggered optimized consensus tracking control problem for uncertain stochastic nonlinear multi-agent systems (MASs) with unknown dynamic and time-delay. Typically, optimal control is derived by the solution of the Hamilton-Jacobi-Bellman (HJB) equation, but it is usually challenging to solve this equation since inherent nonlinearity and unknown dynamics. Specifically, the complexity of the MASs in controller design is further exacerbated by the issue of state interdependence. To achieve optimized consensus control, the adaptive dynamic programming strategy is derived using the negative gradient of a simple positive function. As a result, the designed optimized consensus tracking control is relatively simple and can eliminate the persistence excitation (PE) assumption. The fuzzy logic systems (FLSs) are utilized to approximate the current and delayed states of unknown nonlinear functions;the identifier is proposed to estimate the stochastic multi-agent dynamic;the critic and actor FLSs are designed to evaluate control performance and execute control behavior, respectively. Furthermore, the event-triggered control (ETC) method is developed to save transmission load and communication resources. Moreover, we demonstrate that all signals for the MASs are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and that the states of the follower agents can reach consensus with the leader's state. Finally, a numerical example is illustrated to demonstrate the effectiveness of the proposed method. Note to Practitioners-With environmental protection and energy conservation becoming dominant trends, improving efficiency is regarded as a fundamental principle in control design. In addition, MASs are widely affected by factors such as stochastic disturbance, model unknown, time-delay, and uncertain factors, which further increase the difficulty of controller design. In this work, the optimized control approach is deve

关键词： Stochastic processes Optimal control Fuzzy logic dynamic programming Consensus control Artificial neural networks Vehicle dynamics Uncertainty Mathematical models Training Stochastic multiagent systems optimized consensus control event-triggered control identifier-actor-critic architecture fuzzy logic systems adaptive dynamic programming

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Optimal finite-horizon tracking control in affine nonlinear systems: A Stackelberg game approach with H2/H∞ framework

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APPLIED MATHEMATICS AND COMPUTATION 2025年 495卷

作者： Dong, Xu Zhang, Huaguang Ming, Zhongyang Luo, Yanhong Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110004 Liaoning Peoples R China

In this paper, we address the finite-time optimal tracking control problem within the context of a Stackelberg game structure, characterized by the mixed H2/H infinity framework. This objective is accomplished through the innovative design and implementation of a novel adaptive dynamic programming (ADP) algorithm. Initially, we establish a time-varying coupled Hamilton-Jacobi- Isaacs (HJI) equations, posing a significant challenge in deriving an analytical solution for the optimal leader. Subsequently, we elucidate the existence of Nash equilibrium points, confirming the algorithm's convergence and providing theoretical foundations for its practical application. Furthermore, we introduce a novel ADP algorithm that incorporates time-varying activation functions. The use of the Lyapunov direct method ensures the stability of the closed-loop affine nonlinear system under the ADP control scheme, thereby guaranteeing the system's uniformly ultimately bounded (UUB). Finally, the effectiveness of the aforementioned ADP-based control approach is validated through numerical simulations.

关键词： adaptive dynamic programming Stackelberg game Mixed H2/H infinity control Finite-horizon Neural networks (NNs)

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A novel adaptive dynamic optimal balance control method for wheel-legged robot

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APPLIED MATHEMATICAL MODELLING 2025年 137卷

作者： Liu, Xuefei Sun, Yi Han, Qingfei Cao, Kai Shen, Huan Xu, Jiajun Li, Youfu Ji, Aihong Nanjing Univ Aeronaut & Astronaut Coll Mech & Elect Engn Lab Locomot Bioinspirat & Intelligent Robots Nanjing 210016 Peoples R China City Univ Hong Kong Dept Mech Engn Hong Kong Peoples R China Jiangsu Key Lab Bion Mat & Equipment Nanjing 210016 Peoples R China Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Aerosp Struct Nanjing 210016 Peoples R China

The wheel-legged robots combine efficient and fast wheeled locomotion with the terrain-adaptive legged locomotion. Inspired by reinforcement learning and adaptive dynamic programming, a novel dynamic optimal balance control method is proposed for wheel-legged robots on uneven terrains. First, the virtual leg length is solved according to the kinematics model of the five-link closed-chain mechanism. In addition, a simplified wheel-legged spring-loaded inverted pendulum model is established to determine the linear state-space expression of the floating-base, virtual leg, and driving wheel. Second, a fast iterative algorithm built upon adaptive dynamic programming and optimal gain matrix is introduced. Using the initial gain matrix and an initial state vector, the online policy iteration learns the initial state data set generated by external disturbances, and the steps of policy evaluation and policy improvement are repeatedly implemented by Kleinman's algorithm. Subsequently, the virtual support force is controlled by the composite control framework for the length of the virtual leg with spring-damping characteristics and roll angle. The input torque for each hip joint is calculated using the virtual model control mapping technology. Finally, the robustness and adaptability of the proposed framework are verified through simulations. This paper presents a novel control method for the future application of wheel-legged robot in complex scenarios.

关键词： Wheel-legged robot adaptive dynamic programming Optimal balance control Policy iteration Virtual model control

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Event-triggered neuro-optimal fault tolerant control for uncertain macro-micro composite stage system with actuator faults

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2025年 145卷

作者： Zhang, Shunchao Zhao, Bo Zhang, Yongwei Guangdong Univ Finance Sch Internet Finance & Informat Engn Guangzhou 510521 Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Beijing Normal Univ Sch Syst Sci Beijing 100875 Peoples R China South China Agr Univ Coll Math & Informat Guangzhou 510642 Peoples R China

This paper develops an event-triggered neuro-optimal fault tolerant control (ETNOFTC) method for an uncertain macro-micro composite stage (MMCS) system with actuator faults. By regarding the MMCS system as a two-player system, its control problem is formulated as a nonzero-sum game which aims to cooperatively stabilize the system with the individual cost functions of all players. To stabilize the faulty MMCS system, we develop an ETNOFTC scheme which consists of two parts, i.e., integral sliding mode control and adaptive dynamic programming-based event-triggered optimal control. An integral sliding mode control method is developed to eliminate the effects of actuator faults and uncertainties, and thus a system equivalent to the nominal system is obtained. Then, by employing the critic-only architecture, the event-triggered Hamilton- Jacobi equation is solved by approximating the coupled cost function to obtain the approximate event-triggered optimal control policy of each player. Furthermore, we prove that the closed-loop MMCS system is asymptotically stable by using the Lyapunov's direct method. Finally, the effectiveness of the developed ETNOFTC scheme is verified.

关键词： adaptive dynamic programming Integral sliding mode control Event-triggered control Macro-micro composite stage systems Actuator faults

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