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arXiv · 1810.11767

Robust Regions of Attraction Generation for State-Constrained Perturbed Discrete-Time Polynomial Systems

Bai Xue·Naijun Zhan·Yangjia Li
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Abstract

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.

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Bai Xue, Naijun Zhan, Yangjia Li. 2018-10-28. Robust Regions of Attraction Generation for State-Constrained Perturbed Discrete-Time Polynomial Systems. https://arxiv.org/abs/1810.11767

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