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Dynamic event-triggered-based single-network ADP optimal tracking control for the unknown nonlinear system with constrained input. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.11.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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2
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Wang X, Deng H, Ye X. Model-free nonlinear robust control design via online critic learning. ISA TRANSACTIONS 2022; 129:446-459. [PMID: 34983736 DOI: 10.1016/j.isatra.2021.12.017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2021] [Revised: 12/10/2021] [Accepted: 12/11/2021] [Indexed: 06/14/2023]
Abstract
Online critic learning or solving robust control problems of complex systems usually requires knowledge about system dynamics. In order to achieve these goals in data-driven method, a new performance index related to the decreasing rate of the conventional cost is designed. The corresponding optimal control policy can be approximated online using a new actor-critic scheme with three neural networks, without depending on initial stable control and knowledge about system dynamics. The learning process and the learned control policy show excellent robustness. Numerical simulations and an inverted pendulum experiment show that compared with benchmark methods, the proposed method relaxes the dependence on initial admissible control and exhibits better disturbance attenuation performance.
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Affiliation(s)
- Xiaoyang Wang
- College of Intelligent Systems Science and Engineering, Harbin Engineering University, 150001 Harbin, China.
| | - Hao Deng
- Pengcheng Laboratory, 518055 Shenzhen, China.
| | - Xiufen Ye
- College of Intelligent Systems Science and Engineering, Harbin Engineering University, 150001 Harbin, China.
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Wang X, Quan Z, Li Y, Liu Y. Event-triggered trajectory-tracking guidance for reusable launch vehicle based on neural adaptive dynamic programming. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07468-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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4
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Qin C, Qiao X, Wang J, Zhang D. Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances. ENTROPY 2022; 24:e24060816. [PMID: 35741537 PMCID: PMC9222594 DOI: 10.3390/e24060816] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Revised: 06/07/2022] [Accepted: 06/07/2022] [Indexed: 02/04/2023]
Abstract
In this paper, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the tracking control problems with uncertain disturbances is described as the problem of robust control adjustment. In addition, considering the nominal system of the augmented system, the guaranteed cost tracking control problem is transformed into the optimal control problem by using the discount coefficient in the nominal system. A new safe Hamilton-Jacobi-Bellman (HJB) equation is proposed by combining the cost function with the control barrier function (CBF), so that the behavior of violating the safety regulations for the system states will be punished. In order to solve the new safe HJB equation, a critic neural network (NN) is used to approximate the solution of the safe HJB equation. According to the Lyapunov stability theory, in the case of state constraints and uncertain disturbances, the system states and the parameters of the critic neural network are guaranteed to be uniformly ultimately bounded (UUB). At the end of this paper, the feasibility of the proposed method is verified by a simulation example.
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5
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Robust Tracking Control for Non-Zero-Sum Games of Continuous-Time Uncertain Nonlinear Systems. MATHEMATICS 2022. [DOI: 10.3390/math10111904] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this paper, a new adaptive critic design is proposed to approximate the online Nash equilibrium solution for the robust trajectory tracking control of non-zero-sum (NZS) games for continuous-time uncertain nonlinear systems. First, the augmented system was constructed by combining the tracking error and the reference trajectory. By modifying the cost function, the robust tracking control problem was transformed into an optimal tracking control problem. Based on adaptive dynamic programming (ADP), a single critic neural network (NN) was applied for each player to solve the coupled Hamilton–Jacobi–Bellman (HJB) equations approximately, and the obtained control laws were regarded as the feedback Nash equilibrium. Two additional terms were introduced in the weight update law of each critic NN, which strengthened the weight update process and eliminated the strict requirements for the initial stability control policy. More importantly, in theory, through the Lyapunov theory, the stability of the closed-loop system was guaranteed, and the robust tracking performance was analyzed. Finally, the effectiveness of the proposed scheme was verified by two examples.
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6
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Tu Y, Fang H, Yin Y, He S. Reinforcement learning-based nonlinear tracking control system design via LDI approach with application to trolley system. Neural Comput Appl 2022. [DOI: 10.1007/s00521-021-05909-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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7
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Liu C, Zhang H, Luo Y, Su H. Dual Heuristic Programming for Optimal Control of Continuous-Time Nonlinear Systems Using Single Echo State Network. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:1701-1712. [PMID: 32396118 DOI: 10.1109/tcyb.2020.2984952] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This article presents an improved online adaptive dynamic programming (ADP) algorithm to solve the optimal control problem of continuous-time nonlinear systems with infinite horizon cost. The Hamilton-Jacobi-Bellman (HJB) equation is iteratively approximated by a novel critic-only structure which is constructed using the single echo state network (ESN). Inspired by the dual heuristic programming (DHP) technique, ESN is designed to approximate the costate function, then to derive the optimal controller. As the ESN is characterized by the echo state property (ESP), it is proved that the ESN can successfully approximate the solution to the HJB equation. Besides, to eliminate the requirement for the initial admissible control, a new weight tuning law is designed by adding an alternative condition. The stability of the closed-loop optimal control system and the convergence of the out weights of the ESN are guaranteed by using the Lyapunov theorem in the sense of uniformly ultimately bounded (UUB). Two simulation examples, including linear system and nonlinear system, are given to illustrate the availability and effectiveness of the proposed approach by comparing it with the polynomial neural-network scheme.
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Wang D, Qiao J, Cheng L. An Approximate Neuro-Optimal Solution of Discounted Guaranteed Cost Control Design. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:77-86. [PMID: 32175887 DOI: 10.1109/tcyb.2020.2977318] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The adaptive optimal feedback stabilization is investigated in this article for discounted guaranteed cost control of uncertain nonlinear dynamical systems. Via theoretical analysis, the guaranteed cost control problem involving a discounted utility is transformed to the design of a discounted optimal control policy for the nominal plant. The size of the neighborhood with respect to uniformly ultimately bounded stability is discussed. Then, for deriving the approximate optimal solution of the modified Hamilton-Jacobi-Bellman equation, an improved self-learning algorithm under the framework of adaptive critic designs is established. It facilitates the neuro-optimal control implementation without an additional requirement of the initial admissible condition. The simulation verification toward several dynamics is provided, involving the F16 aircraft plant, in order to illustrate the effectiveness of the discounted guaranteed cost control method.
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Online event-based adaptive critic design with experience replay to solve partially unknown multi-player nonzero-sum games. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.05.087] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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10
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Ma B, Li Y. Compensator-critic structure-based event-triggered decentralized tracking control of modular robot manipulators: theory and experimental verification. COMPLEX INTELL SYST 2021. [DOI: 10.1007/s40747-021-00359-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
AbstractThis paper presents a novel compensator-critic structure-based event-triggered decentralized tracking control of modular robot manipulators (MRMs). On the basis of subsystem dynamics under joint torque feedback (JTF) technique, the proposed tracking error fusion function, which includes position error and velocity error, is utilized to construct performance index function. By analyzing the dynamic uncertainties, a local dynamic information-based robust controller is designed to engage the model uncertainty compensation. Based on adaptive dynamic programming (ADP) algorithm and the event-triggered mechanism, the decentralized tracking control is obtained by solving the event-triggered Hamilton–Jacobi–Bellman equation (HJBE) with the critic neural network (NN). The tracking error of the closed-loop manipulators system is proved to be ultimately uniformly bounded (UUB) using the Lyapunov stability theorem. Finally, experimental results illustrate the effectiveness of the developed control method.
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Yang X, He H. Decentralized Event-Triggered Control for a Class of Nonlinear-Interconnected Systems Using Reinforcement Learning. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:635-648. [PMID: 31670691 DOI: 10.1109/tcyb.2019.2946122] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In this article, we propose a novel decentralized event-triggered control (ETC) scheme for a class of continuous-time nonlinear systems with matched interconnections. The present interconnected systems differ from most of the existing interconnected plants in that their equilibrium points are no longer assumed to be zero. Initially, we establish a theorem to indicate that the decentralized ETC law for the overall system can be represented by an array of optimal ETC laws for nominal subsystems. Then, to obtain these optimal ETC laws, we develop a reinforcement learning (RL)-based method to solve the Hamilton-Jacobi-Bellman equations arising in the discounted-cost optimal ETC problems of the nominal subsystems. Meanwhile, we only use critic networks to implement the RL-based approach and tune the critic network weight vectors by using the gradient descent method and the concurrent learning technique together. With the proposed weight vectors tuning rule, we are able to not only relax the persistence of the excitation condition but also ensure the critic network weight vectors to be uniformly ultimately bounded. Moreover, by utilizing the Lyapunov method, we prove that the obtained decentralized ETC law can force the entire system to be stable in the sense of uniform ultimate boundedness. Finally, we validate the proposed decentralized ETC strategy through simulations of the nonlinear-interconnected systems derived from two inverted pendulums connected via a spring.
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12
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Neural networks-based optimal tracking control for nonzero-sum games of multi-player continuous-time nonlinear systems via reinforcement learning. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.06.083] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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13
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Zhao B, Shi G, Wang D. Asymptotically stable critic designs for approximate optimal stabilization of nonlinear systems subject to mismatched external disturbances. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2018.08.092] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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14
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Neural Network-Based Optimal Tracking Control of Continuous-Time Uncertain Nonlinear System via Reinforcement Learning. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10220-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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15
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Xia R, Chen M, Wu Q, Wang Y. Neural network based integral sliding mode optimal flight control of near space hypersonic vehicle. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.10.038] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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16
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An Analysis of IRL-Based Optimal Tracking Control of Unknown Nonlinear Systems with Constrained Input. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10029-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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17
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Fuzzy adaptive dynamic programming-based optimal leader-following consensus for heterogeneous nonlinear multi-agent systems. Neural Comput Appl 2019. [DOI: 10.1007/s00521-019-04263-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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18
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Liu C, Zhang H, Xiao G, Sun S. Integral reinforcement learning based decentralized optimal tracking control of unknown nonlinear large-scale interconnected systems with constrained-input. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.09.011] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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19
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Wang D, Liu D. Learning and Guaranteed Cost Control With Event-Based Adaptive Critic Implementation. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:6004-6014. [PMID: 29993846 DOI: 10.1109/tnnls.2018.2817256] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper focuses on the event-triggered guaranteed cost control design of nonlinear systems via a self-learning technique. In brief, an event-based guaranteed cost control strategy of nonlinear systems subjects to matched uncertainties is developed, thereby balancing the performance of guaranteed cost and the actuality of limited communication resource. The original control design is transformed into an optimal control problem with an event-based mechanism, where the relationship of guaranteed cost performance compared to the time-based formulation is discussed. A critic neural network is constructed for implementing the event-based optimal control design with stability guarantee. Simulation experiments are carried out to verify the theoretical results in detail.
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20
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Decentralized robust optimal control for modular robot manipulators via critic-identifier structure-based adaptive dynamic programming. Neural Comput Appl 2018. [DOI: 10.1007/s00521-018-3714-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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21
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Fan B, Yang Q, Tang X, Sun Y. Robust ADP Design for Continuous-Time Nonlinear Systems With Output Constraints. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:2127-2138. [PMID: 29771666 DOI: 10.1109/tnnls.2018.2806347] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In this paper, a novel robust adaptive dynamic programming (RADP)-based control strategy is presented for the optimal control of a class of output-constrained continuous-time unknown nonlinear systems. Our contribution includes a step forward beyond the usual optimal control result to show that the output of the plant is always within user-defined bounds. To achieve the new results, an error transformation technique is first established to generate an equivalent nonlinear system, whose asymptotic stability guarantees both the asymptotic stability and the satisfaction of the output restriction of the original system. Furthermore, RADP algorithms are developed to solve the transformed nonlinear optimal control problem with completely unknown dynamics as well as a robust design to guarantee the stability of the closed-loop systems in the presence of unavailable internal dynamic state. Via small-gain theorem, asymptotic stability of the original and transformed nonlinear system is theoretically guaranteed. Finally, comparison results demonstrate the merits of the proposed control policy.
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22
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Self-learning robust optimal control for continuous-time nonlinear systems with mismatched disturbances. Neural Netw 2018; 99:19-30. [DOI: 10.1016/j.neunet.2017.11.022] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Revised: 10/16/2017] [Accepted: 11/28/2017] [Indexed: 11/19/2022]
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23
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Dong B, Zhou F, Liu K, Li Y. Torque sensorless decentralized neuro-optimal control for modular and reconfigurable robots with uncertain environments. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.12.012] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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24
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Jiang H, Zhang H. Iterative ADP learning algorithms for discrete-time multi-player games. Artif Intell Rev 2018. [DOI: 10.1007/s10462-017-9603-1] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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25
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Wang D, Liu D, Zhang Y, Li H. Neural network robust tracking control with adaptive critic framework for uncertain nonlinear systems. Neural Netw 2018; 97:11-18. [DOI: 10.1016/j.neunet.2017.09.005] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2017] [Revised: 07/18/2017] [Accepted: 09/04/2017] [Indexed: 11/16/2022]
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26
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Wang D, Mu C. A novel neural optimal control framework with nonlinear dynamics: Closed-loop stability and simulation verification. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.05.051] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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27
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Wang D, He H, Liu D. Adaptive Critic Nonlinear Robust Control: A Survey. IEEE TRANSACTIONS ON CYBERNETICS 2017; 47:3429-3451. [PMID: 28682269 DOI: 10.1109/tcyb.2017.2712188] [Citation(s) in RCA: 80] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Adaptive dynamic programming (ADP) and reinforcement learning are quite relevant to each other when performing intelligent optimization. They are both regarded as promising methods involving important components of evaluation and improvement, at the background of information technology, such as artificial intelligence, big data, and deep learning. Although great progresses have been achieved and surveyed when addressing nonlinear optimal control problems, the research on robustness of ADP-based control strategies under uncertain environment has not been fully summarized. Hence, this survey reviews the recent main results of adaptive-critic-based robust control design of continuous-time nonlinear systems. The ADP-based nonlinear optimal regulation is reviewed, followed by robust stabilization of nonlinear systems with matched uncertainties, guaranteed cost control design of unmatched plants, and decentralized stabilization of interconnected systems. Additionally, further comprehensive discussions are presented, including event-based robust control design, improvement of the critic learning rule, nonlinear H∞ control design, and several notes on future perspectives. By applying the ADP-based optimal and robust control methods to a practical power system and an overhead crane plant, two typical examples are provided to verify the effectiveness of theoretical results. Overall, this survey is beneficial to promote the development of adaptive critic control methods with robustness guarantee and the construction of higher level intelligent systems.
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Neural-network-based adaptive guaranteed cost control of nonlinear dynamical systems with matched uncertainties. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.03.047] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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29
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General value iteration based reinforcement learning for solving optimal tracking control problem of continuous–time affine nonlinear systems. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.03.038] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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30
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Qu Q, Zhang H, Feng T, Jiang H. Decentralized adaptive tracking control scheme for nonlinear large-scale interconnected systems via adaptive dynamic programming. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.10.058] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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31
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Distributed learning for feedforward neural networks with random weights using an event-triggered communication scheme. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.10.059] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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32
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Lyapunov stability-based control and identification of nonlinear dynamical systems using adaptive dynamic programming. Soft comput 2017. [DOI: 10.1007/s00500-017-2500-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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33
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Wang D, Mu C, Zhang Q, Liu D. Event-based input-constrained nonlinear H∞ state feedback with adaptive critic and neural implementation. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.07.002] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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34
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Wang D, Liu D, Mu C, Ma H. Decentralized guaranteed cost control of interconnected systems with uncertainties: A learning-based optimal control strategy. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.06.020] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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35
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Yang X, Liu D, Luo B, Li C. Data-based robust adaptive control for a class of unknown nonlinear constrained-input systems via integral reinforcement learning. Inf Sci (N Y) 2016. [DOI: 10.1016/j.ins.2016.07.051] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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