Approximately Optimal Control of Discrete-Time Nonlinear Switched Systems Using Globalized Dual Heuristic Programming
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Approximately Optimal Control of Discrete-Time Nonlinear Switched Systems Using Globalized Dual Heuristic Programming Chaoxu Mu1 · Kaiju Liao1 · Ling Ren1 · Zhongke Gao1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Based on the idea of data-driven control, a novel iterative adaptive dynamic programming (ADP) algorithm based on the globalized dual heuristic programming (GDHP) technique is used to solve the optimal control problem of discrete-time nonlinear switched systems. In order to solve the Hamilton–Jacobi–Bellman (HJB) equation of switched systems, the iterative ADP method is proposed and the strict convergence analysis is also provided. Three neural networks are constructed to implement the iterative ADP algorithm, where a novel model network is designed to identify the system dynamics, a critic network is used to approximate the cost function and its partial derivatives, and an action network is provided to obtain the approximate optimal control law. Two simulation examples are described to illustrate the effectiveness of the proposed method by comparing with the heuristic dynamic programming (HDP) and dual heuristic programming (DHP) methods. Keywords Globalized dual heuristic programming (GDHP) · Optimal control · Switched systems · Neural networks
This work was supported in part by the National Natural Science Foundation of China under Grants 61773284 and 61873181.
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Zhongke Gao [email protected] Chaoxu Mu [email protected] Kaiju Liao [email protected] Ling Ren [email protected]
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School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
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C. Mu et al.
1 Introduction The switched system is a kind of hybrid control system consisting of two or more subsystems, which has been widely studied and applied in power systems, robot systems, traffic control systems and process control systems [1–5]. In the previous studies, researches often focused on the nature of the switched system itself, such as the stability and the controllability [6–9]. With the development of switched system theory, the optimal control problem has attracted extensive attention. For the optimal control problem of switched systems, not only the optimal control law should be studied, but also the optimal switched sequence should be considered [10–12]. For example, Carla et al. [10] proposed two different optimal control methods for switched affine systems by minimizing the performance index. In [11], the optimal control problem was transformed into an equivalent parameterized problem to obtain the optimal solution for linear switched systems. Liu and Gong [12] gave an optimal control method for autonomous systems and proposed a computational scheme to find the optimal switching instants. It is well known that the dynamic programming (DP) algorithm is one of the useful methods to solve the optimal control problem [13–15]. Effati et al. [14] provided an iterative DP algorithm to solve the nonlinear differential equations and proved the effectiveness of the pro
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