Policy Iteration for H infinity Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming
Zhu, Yuanheng1,2; Zhao, Dongbin1,2; Yang, Xiong3; Zhang, Qichao1,2
2018-02-01
发表期刊IEEE TRANSACTIONS ON CYBERNETICS
卷号48期号:2页码:500-509
文章类型Article
摘要Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the H infinity optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest L-2-gain and the associated H infinity optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.
关键词Adaptive Dynamic Programming (Adp) h Infinity Optimal Control Policy Iteration (Pi) Polynomial Nonlinear Systems Sum Of Squares (Sos)
WOS标题词Science & Technology ; Technology
DOI10.1109/TCYB.2016.2643687
关键词[WOS]STATE-FEEDBACK CONTROL ; DISCRETE-TIME-SYSTEMS ; ALGORITHM ; DYNAMICS ; EQUATION ; UPDATE
收录类别SCI
语种英语
项目资助者National Natural Science Foundation of China(61603382 ; Early Career Development Award of SKLMCCS ; 61273136 ; 61573353 ; 61533017 ; 61503379)
WOS研究方向Automation & Control Systems ; Computer Science
WOS类目Automation & Control Systems ; Computer Science, Artificial Intelligence ; Computer Science, Cybernetics
WOS记录号WOS:000422925700005
引用统计
文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/21937
专题复杂系统管理与控制国家重点实验室_深度强化学习
作者单位1.Chinese Acad Sci, Inst Automat, State Key Lab Management & Control Complex Syst, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
3.Tianjin Univ, Sch Elect Engn & Automat, Tianjin 300072, Peoples R China
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Zhu, Yuanheng,Zhao, Dongbin,Yang, Xiong,et al. Policy Iteration for H infinity Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming[J]. IEEE TRANSACTIONS ON CYBERNETICS,2018,48(2):500-509.
APA Zhu, Yuanheng,Zhao, Dongbin,Yang, Xiong,&Zhang, Qichao.(2018).Policy Iteration for H infinity Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.IEEE TRANSACTIONS ON CYBERNETICS,48(2),500-509.
MLA Zhu, Yuanheng,et al."Policy Iteration for H infinity Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming".IEEE TRANSACTIONS ON CYBERNETICS 48.2(2018):500-509.
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