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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Xue, Bai Zhan, Naijun Li, Yangjia Univ Chinese Acad Sci Beijing Peoples R China Chinese Acad Sci State Key Lab Comp Sci Inst Software Beijing Peoples R China

In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that every possible trajectory initialized in it will approach an equilibrium state while never violating the specified state constraint, regardless of the actual perturbation. Based on a Hellman equation which characterizes the interior of the maximal robust region of attraction as the strict one sub-level set of its unique bounded and continuous solution, we construct a semi-definite program for computing robust regions of attraction. Under appropriate assumptions, the existence of solutions to the constructed semi-definite program is guaranteed and there exists a sequence of solutions such that their strict one sub-level sets inner-approximate and converge to the interior of the maximal robust region of attraction in measure. Finally, we demonstrate the method by two examples. Copyright (C) 2020 The Authors.

关键词： Robust Regions of Attraction state-constrained perturbed discrete-time polynomial systems Convex Programming

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Robust Regions of Attraction Generation for state-constrained perturbed discrete-time polynomial systems

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IFAC-PapersOnLine 2020年第2期53卷 6327-6333页

作者： Bai Xue Naijun Zhan Yangjia Li University of Chinese Academy of Sciences Beijing China State Key Lab. of Computer Science Institute of Software CAS China

In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that every possible trajectory initialized in it will approach an equilibrium state while never violating the specified state constraint, regardless of the actual perturbation. Based on a Bellman equation which characterizes the interior of the maximal robust region of attraction as the strict one sub-level set of its unique bounded and continuous solution, we construct a semi-definite program for computing robust regions of attraction. Under appropriate assumptions, the existence of solutions to the constructed semi-definite program is guaranteed and there exists a sequence of solutions such that their strict one sub-level sets inner-approximate and converge to the interior of the maximal robust region of attraction in measure. Finally, we demonstrate the method by two examples.

关键词： Robust Regions of Attraction state-constrained perturbed discrete-time polynomial systems Convex Programming

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