Extended adaptive optimal control of linear systems with unknown dynamics using adaptive dynamic programming

Gan, Minggang; Zhao, Jingang; Zhang, Chi

doi:10.1002/asjc.2243

Cited by 15 publications

(17 citation statements)

References 28 publications

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“…Recently, adaptive/approximate dynamic programming (ADP) has been proposed as a method of solving optimal control problems in which NNs are trained to approximately solve the problem of interest [3,[8][9][10]. The basic ADP framework has three types of components: (1) critics, (2) models, and (3) actions.…”

Section: Introductionmentioning

confidence: 99%

Solution for optimal control of general nonlinear systems using generating functions

Wang

Liang

et al. 2022

Asian Journal of Control

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In this paper, we present an analytical local solution for optimal control problems applicable to a wide class of general nonlinear systems. We first introduce the optimal control problem for a general nonlinear system and formulate the associated Hamilton-Jacobi-Bellman equation. Starting from the necessary conditions for optimality represented by the Hamiltonian system of the optimal control problem, we solve the Hamilton-Jacobi equation for the associated generating functions. The generating functions are obtained in the form of series expansions by using canonical transformation theory and the semitensor product of matrices. The coefficients of the generating functions satisfy simply the algebraic Riccati equation and linear algebraic equations for the second-degree homogeneous component and higher degree components, respectively, from which an algorithm and data structure can be derived. This enables us to obtain analytical optimal feedback controllers and the corresponding Lyapunov function. Through theoretical analysis, it is established that the proposed methodology guarantees stability of the closedloop system. This approach is not affected by the complexity of the performance index and state equations, and most importantly, it does not require any initial admissible control law. A simulation example is presented to illustrate the effectiveness and applicability of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Solution for optimal control of general nonlinear systems using generating functions

Wang

Liang

et al. 2022

Asian Journal of Control

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“…Furthermore, this control scheme is widely used to control linear and nonlinear systems [9]. The adaptive control has been integrated with classical and advanced control schemes such as PID [3], SMC [7], optimal control [10], fuzzy control [11], event-triggered control [12], neural network control [13]. Since sliding mode control is highly robust against uncertainties, while adaptive control can deal with unknown dynamics.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Fractional High‐order Terminal Sliding Mode Control for Nonlinear Robotic Manipulator under Alternating Loads

Ahmed

Wang

Tian

2020

Asian Journal of Control

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In this study, trajectory tracking of robotic manipulators under varying loads with uncertainties and external disturbances is obtained by proposing model-independent adaptive fractional high-order terminal sliding mode control (AFO-HoTSMC). The proposed AFO-HoTSMC method is composed of an adaptive high-order terminal sliding mode control integrated with fractional-order (FO) control. An adaptive tuning control is utilised to evaluate the uncertain unknown dynamics of the system without relying on the prior knowledge of the upper bounds. FO control and HoTSMC are used to achieve the fast finite-time convergence, chatter-free control inputs, better tracking performance and robustness. The finite-time stability of the overall system is investigated and derived from the Lyapunov stability criterion. Finally, to validate the effectiveness and robustness of the developed control method, comparative simulations with H ∞ -Adaptive control, intelligent PD (iPD), intelligent PID (iPID) and adaptive third-order SMC (ATOSMC) are realized to demonstrate the performance of AFO-HoTSMC.

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“…Reinforcement learning is a biologically inspired approximate method and has certain advantages in coping with optimization problems with uncertainty models or unknown dynamics. Adaptive dynamic programming [8][9][10][11] and approximate dynamic programming (ADP) [12][13][14][15] also belong to the category of reinforcement learning, and overcome the deficiencies of traditional dynamic programming, such as the curse of modelling and the curse of dimensionality [16,17].…”

Section: Introductionmentioning

confidence: 99%

Neural network‐based optimal tracking control for partially unknown discrete‐time non‐linear systems using reinforcement learning

Zhao

Vishal

2020

IET Control Theory & Appl

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Otimal tracking control of discrete‐time non‐linear systems is investigated in this paper. The system drift dynamics is unknown in this investigation. Firstly, in the light of the discrete‐time non‐linear systems and reference signal, an augmented system is constructed. Optimal tracking control problem of original non‐linear systems is thus transformed into solving optimal regulation problem of the augmented systems. The solution to optimal regulation problem can be found by solving its Hamilton–Jacobi–Bellman (HJB) equation. To solve the HJB equation, a new critic‐actor neural network (NN) structure‐based online reinforcement learning (RL) scheme is proposed to learn the solution of HJB equation while the corresponding optimal control input that minimizes the HJB equation is calculated in a forward‐in‐time manner without requiring any value, policy iterations and the system drift dynamics. The Uniformly Ultimately Boundedness (UUB) of NN weight errors and closed‐loop augmented system states are provided via the Lyapunov theory. Finally, simulation results are given to validate the proposed scheme.

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Extended adaptive optimal control of linear systems with unknown dynamics using adaptive dynamic programming

Cited by 15 publications

References 28 publications

Solution for optimal control of general nonlinear systems using generating functions

Solution for optimal control of general nonlinear systems using generating functions

Adaptive Fractional High‐order Terminal Sliding Mode Control for Nonlinear Robotic Manipulator under Alternating Loads

Neural network‐based optimal tracking control for partially unknown discrete‐time non‐linear systems using reinforcement learning

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