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optimal tracking control of Second-Order Multiagent Systems With Input Delay via Data-Driven Forward Reward Q -Learning Framework

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年第3期55卷 1858-1869页

作者： Rao, Kai Yan, Huaicheng Liu, Qiwei Dang, Qingmei Shi, Kaibo East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Minist Educ Shanghai 200237 Peoples R China East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Minist Educ Shanghai 200237 Peoples R China Weifang Univ Coll Machinery & Automat Weifang 261061 Peoples R China Beijing Univ Chem Technol Coll Informat Sci & Technol Beijing 100029 Peoples R China Chengdu Univ Sch Elect Informat & Elect Engn Chengdu 610106 Peoples R China

In this article, an optimal tracking control algorithm is derived for second-order discrete-time multiagent systems (MASs) with unknown system dynamics and input delay. First, the optimal tracking problem of MASs with input delay is constructed by the tracking error and a local performance index function. By designing a new variable, the original model is converted into a model without delay while guaranteeing the equivalence of performance index and control law of each agent. Subsequently, the transformed model and reinforcement learning (RL) theory are integrated to obtain a novel data-driven distributed learning framework. This framework enables online learning of the optimal control law and ensures tracking consensus of all followers' position and velocity states. Compared to the traditional actor-critic framework, an additional neural network (NN) is utilized to approximate the forward reward information (FRI) to improve the information learning capability of the MASs. Furthermore, the convergence analysis of system states and three NNs structures are conducted by Lyapunov theory. Finally, the proposed framework is verified to have better convergence and require fewer iteration steps than classical actor-critic framework by numerical simulation comparison experiments.

关键词： Delays Heuristic algorithms Performance analysis Convergence Q-learning optimal control Artificial neural networks Approximation algorithms Delay effects System dynamics Data-driven input delays optimal tracking control reinforcement learning (RL) second-order multiagent systems (MASs)

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Reinforcement learning-based optimal tracking control for uncertain multi-agent systems with uncertain topological networks

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ISA TRANSACTIONS 2025年 156卷 217-227页

作者： You, Renyang Liu, Quan Soochow Univ Sch Comp Sci & Technol Suzhou 215006 Peoples R China

Recent decades, extensive applications exemplified in intelligent connected vehicles (ICVs) and unmanned aerial vehicles (UAVs) have emerged with the rapidly development of multi-agent systems (MASs). Inspired by these applications, the optimal tracking control problem for uncertain MASs under uncertain topological networks is addressed based on the theory of observer design and reinforcement learning (RL). Thus, an adaptive extended observer based on concurrent learning (CL) technique is designed to simultaneously estimate system states and unknown parameters, where unknown parameters estimated convergence is guaranteed in a relaxed persistence of excitation condition. Moreover, a Luenberger observer is designed to estimate the state of the leader under uncertain topological networks, which acts as the information compensation of the leader. Via the proposed observers, an optimal tracking control algorithm is devised leveraging actor-critic (AC)- neural network (NN), which does not require the state derivative information. Lastly, a numerical simulation is performed to demonstrate the validity of the scheme in question.

关键词： optimal tracking control Uncertain multi-agent systems Uncertain topological networks Reinforcement learning Concurrent learning Actor-critic neural network

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Sliding optimal tracking control of Autonomous Underwater Vehicles With Adaptive Dynamic Programming

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2025年第2期61卷 3361-3372页

作者： Miao, Baixue Lv, Yongfeng Chang, Huimin Ren, Xuemei Taiyuan Univ Technol Coll Elect & Power Engn Taiyuan 030024 Peoples R China Shanxi Univ Sch Math Sci Taiyuan 030006 Peoples R China Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

To improve the tracking performance of autonomous underwater vehicles (AUVs), a sliding optimal tracking control method for linear continuous systems is proposed with adaptive dynamic programming. The AUV vertical dynamic model is constructed with the kinematic principle first. The tracking model is then transformed into a linear sliding model, and the optimal feedback tracking controller is established. Considering the tracking performance of the AUV and the transient performance of the AUV, an adaptive Riccati equation is linearly parameterized, and an online learning algorithm driven by a parameter estimation error is introduced to study the optimal solution of the algebraic Riccati equation. Finally, the stability of the closed-loop system and the estimation convergence of the sliding model are proved by Lyapunov theory. Simulation results demonstrate that the proposed method effectively achieves sliding optimal tracking performance with good dynamic response, high tracking accuracy, and robustness.

关键词： Adaptation models optimal control Mathematical models Vectors Interference Dynamic programming Aerospace and electronic systems Vehicle dynamics Sliding mode control Robustness Adaptive dynamic programming (ADP) adaptive law autonomous underwater vehicle (AUV) optimal tracking control sliding-mode technology

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Lifelong Safe optimal Adaptive tracking control of Nonlinear Strict-Feedback Discrete-Time Systems

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INTERNATIONAL JOURNAL OF ADAPTIVE control AND SIGNAL PROCESSING 2025年第3期39卷 451-470页

作者： Farzanegan, Behzad Jagannathan, S. Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65409 USA

This paper presents a comprehensive approach for achieving multi-task safe optimal adaptive tracking (MSOAT) for a class of nonlinear discrete-time systems, particularly those in strict-feedback form, utilizing a multi-layer neural network (MNN)-based framework. To begin, a cost function with a novel Barrier function (BF) term is introduced for each subsystem to address the weak safely reachable problem, serving as a crucial tool for guiding the system's trajectory toward the safe set while avoiding unwanted sets. To deal with the tracking problem, the Hamilton-Jacobi-Bellman (HJB) framework is used through the actor-critic MNN-based backstepping technique to estimate the solution of the value functions and obtain both virtual and actual optimal control policies for each subsystem, effectively circumventing non-causality issues. Further, to mitigate catastrophic forgetting in multi-tasking scenarios, a regularizer term, which is derived from the online version of the Elastic Weight Consolidation (EWC) method, is included in the critic and actor MNN update laws without directly computing the Fisher information matrix. To enhance the convergence rate, the critic MNN is tuned with a hybrid learning technique involving weight adjustments both at specific sampling instants and iteratively within those intervals. A control barrier function (CBF) with a time-varying BF is also integrated into the actor update law, collaborating with the BF to keep the trajectory in the safe set with a smaller trade-off factor, simultaneously validating the safety condition in real-time. Finally, the overall stability is established. An example of a 6-DOF autonomous underwater vehicle (AUV) is used to assess the effectiveness of the proposed approach.

关键词： autonomous underwater vehicles backstepping barrier function constraints control barrier function lifelong learning optimal tracking control strict-feedback systems weak safe reachability

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Robust Adaptive optimal tracking Switching control of Nonlinear Systems Using Embedding Transformation and Approximate Dynamic Programming

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INTERNATIONAL JOURNAL OF ADAPTIVE control AND SIGNAL PROCESSING 2025年第5期39卷 1079-1090页

作者： Wang, Weizhe Fu, Yue Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang Peoples R China

For unknown continuous-time nonlinear systems with multiple equilibrium points, this article proposes a robust adaptive optimal tracking switching controller. The controller integrates multiple nonlinear approximate optimal tracking controllers, an optimal switching sequence, and a robust compensator. First, multiple nonlinear neural network models are established to construct a controller design model, whose unknown parameters are online estimated by resorting to Lyapunov stability theory. Then, at every instant, the optimal switching sequence and approximate optimal tracking controller are obtained by using embedding transformation and approximate dynamic programming technology. After that, according to the error between the nonlinear system and the given input, a robust compensator is designed. Finally, stability and convergence of the control system are verified, and the simulations are conducted to validate the effectiveness and superiority.

关键词： adaptive control adaptive dynamic programming (ADP) nonlinear system optimal tracking control switching control

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optimal tracking control for linear time-delay large-scale systems with persistent disturbances

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Journal of Systems Engineering and Electronics 2009年第5期20卷 1058-1064页

作者： Tang Ruichun Ma Huamin Guo Shuangle Ren Lijie Coll. of Information Science and Engineering Ocean Univ. of China Qingdao 266100 P. R. China Huawei Technologies Co. Ltd Shenzhen 518129 P. R. China Coll. of Mathematics and Computer Science Hengshui Univ. Hengshui 053000 P. R. China

An optimal tracking control （OTC） problem for linear time-delay large-scale systems affected by external persistent disturbances is investigated. Based on the internal model principle, a disturbance compensator is constructed. The system with persistent disturbances is transformed into an augmented system without persistent disturbances. The original OTC problem of linear time-delay system is transformed into a sequence of linear two- point boundary value （TPBV） problems by introducing a sensitivity parameter and expanding Maclaurin series around it. By solving an OTC law of the augmented system, the OTC law of the original system is obtained. A numerical simulation is provided to illustrate the effectiveness of the proposed method.

关键词： optimal tracking control sensitivity approach time-delay large-scale system persistent disturbance,

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optimal tracking control of nonlinear partially-unknown constrained-input systems using integral reinforcement learning

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AUTOMATICA 2014年第7期50卷 1780-1792页

作者： Modares, Hamidreza Lewis, Frank L. Univ Texas Arlington Res Inst Ft Worth TX 76118 USA

In this paper, a new formulation for the optimal tracking control problem (OTCP) of continuous-time nonlinear systems is presented. This formulation extends the integral reinforcement learning (IRL) technique, a method for solving optimal regulation problems, to learn the solution to the OTCP. Unlike existing solutions to the OTCP, the proposed method does not need to have or to identify knowledge of the system drift dynamics, and it also takes into account the input constraints a priori. An augmented system composed of the error system dynamics and the command generator dynamics is used to introduce a new nonquadratic discounted performance function for the OTCP. This encodes the input constrains into the optimization problem. A tracking Hamilton-Jacobi-Bellman (HJB) equation associated with this nonquadratic performance function is derived which gives the optimal control solution. An online IRL algorithm is presented to learn the solution to the tracking HJB equation without knowing the system drift dynamics. Convergence to a near-optimal control solution and stability of the whole system are shown under a persistence of excitation condition. Simulation examples are provided to show the effectiveness of the proposed method. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： optimal tracking control Integral reinforcement learning Input constrainers Neural networks

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optimal tracking control for Uncertain Nonlinear Systems With Prescribed Performance via Critic-Only ADP

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第1期52卷 561-573页

作者： Dong, Hongyang Zhao, Xiaowei Luo, Biao Univ Warwick Sch Engn Coventry CV4 7AL W Midlands England Cent South Univ Sch Automat Changsha 410083 Peoples R China

This article addresses the tracking control problem for a class of nonlinear systems described by Euler-Lagrange equations with uncertain system parameters. The proposed control scheme is capable of guaranteeing prescribed performance from two aspects: 1) a special parameter estimator with prescribed-performance properties is embedded in the control scheme. The estimator not only ensures the exponential convergence of the estimation errors under relaxed excitation conditions but also can restrict all estimates to predetermined bounds during the whole estimation process and 2) the proposed controller can strictly guarantee the user-defined performance specifications on tracking errors, including convergence rate, maximum overshoot, and residual set. More importantly, it has the optimizing ability for the tradeoff between performance and control cost. A state transformation method is employed to transform the constrained optimal tracking control problem to an unconstrained stationary optimal problem. Then, a critic-only adaptive dynamic programming algorithm is designed to approximate the solution of the Hamilton-Jacobi-Bellman equation and the corresponding optimal control policy. Uniformly ultimately bounded stability is guaranteed via a Lyapunov-based stability analysis. Finally, numerical simulation results demonstrate the effectiveness of the proposed control scheme.

关键词： Nonlinear systems Convergence Iron Stability analysis Indexes Mathematical model Uncertain systems Adaptive dynamic programming (ADP) optimal tracking control parameter estimation prescribed performance reinforcement learning (RL)

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optimal tracking control for Discrete-time Systems with Multiple Input Delays under Sinusoidal Disturbances

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INTERNATIONAL JOURNAL OF control AUTOMATION AND SYSTEMS 2015年第2期13卷 292-301页

作者： Han, Shi-Yuan Wang, Dong Chen, Yue-Hui Tang, Gong-You Yang, Xi-Xin Univ Jinan Shandong Prov Key Lab Network Based Intelligent C Jinan 250022 Peoples R China Ocean Univ China Coll Informat Sci & Engn Qingdao 266100 Peoples R China Qingdao Univ Coll Software Tech Qingdao 266100 Peoples R China

This study researches the tracking control problem for discrete-time systems with multiple input delays affected by sinusoidal disturbances. This study is organized around the expression of sinusoidal and disturbances and the delay-free transformation. First, based on the periodic characteristic of the sinusoidal disturbance, the sinusoidal disturbances are considered as the output of an exosystem. By proposing a discrete variable transformation, the discrete-time system with multiple input delays and the quadratic performance index are transformed into equivalent delay-free ones. Then, by constructing an augmented system that comprises the states of the exosystems of sinusoidal disturbances, the reference input, and the delay-free transformation systems, the original tracking problem is transformed into the optimal tracking problem for a delay-free system with respect to the simplified performance index. The optimal tracking control (OTC) law is obtained from Riccati and Stein equations. The existent and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the problem of physically realizable for the items of the reference input and sinusoidal disturbances. Finally, the feasibility and effectiveness of the proposed approaches are validated by numerical examples.

关键词： Discrete-time systems multiple input delays observer optimal tracking control sinusoidal disturabnces

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optimal tracking control of Nonlinear Multiagent Systems Using Internal Reinforce Q-Learning

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022年第8期33卷 4043-4055页

作者： Peng, Zhinan Luo, Rui Hu, Jiangping Shi, Kaibo Nguang, Sing Kiong Ghosh, Bijoy Kumar Univ Elect Sci & Technol China Sch Automat Engn Chengdu 611731 Peoples R China Chengdu Univ Sch Informat Sci & Engn Chengdu 610106 Peoples R China Univ Auckland Dept Elect Comp & Software Engn Auckland 1142 New Zealand Texas Tech Univ Dept Math & Stat Lubbock TX 79409 USA

In this article, a novel reinforcement learning (RL) method is developed to solve the optimal tracking control problem of unknown nonlinear multiagent systems (MASs). Different from the representative RL-based optimal control algorithms, an internal reinforce Q-learning (IrQ-L) method is proposed, in which an internal reinforce reward (IRR) function is introduced for each agent to improve its capability of receiving more long-term information from the local environment. In the IrQL designs, a Q-function is defined on the basis of IRR function and an iterative IrQL algorithm is developed to learn optimally distributed control scheme, followed by the rigorous convergence and stability analysis. Furthermore, a distributed online learning framework, namely, reinforce-critic-actor neural networks, is established in the implementation of the proposed approach, which is aimed at estimating the IRR function, the Q-function, and the optimal control scheme, respectively. The implemented procedure is designed in a data-driven way without needing knowledge of the system dynamics. Finally, simulations and comparison results with the classical method are given to demonstrate the effectiveness of the proposed tracking control method.

关键词： optimal control Mathematical model Heuristic algorithms Iterative algorithms Artificial neural networks Nonlinear dynamical systems Multi-agent systems Neural networks (NNs) nonlinear multiagent systems (MASs) optimal tracking control reinforcement learning (RL)

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