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arXiv · 1812.10588

Synthesizing Robust Domains of Attraction for State-Constrained Perturbed Polynomial Systems

Bai Xue·Qiuye Wang·Naijun Zhan·Shijie Wang·Zhikun She
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Abstract

In this paper we propose a novel semi-definite programming based method to compute robust domains of attraction for state-constrained perturbed polynomial systems. A robust domain of attraction is a set of states such that every trajectory starting from it will approach an equilibrium while never violating a specified state constraint, regardless of the actual perturbation. The semi-definite program is constructed by relaxing a generalized Zubov's equation. 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 the interior of the maximal robust domain of attraction in measure under appropriate assumptions. Some illustrative examples demonstrate the performance of our method.

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Bai Xue, Qiuye Wang, Naijun Zhan, Shijie Wang, Zhikun She. 2018-12-27. Synthesizing Robust Domains of Attraction for State-Constrained Perturbed Polynomial Systems. https://arxiv.org/abs/1812.10588

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