2018/12/27 by Xue Bai, Xue, Bai, Qiuye Wang +7 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #Algorithm #Applied mathematics #Attraction #Computer science #Constraint (computer-aided design) #Domain (mathematical analysis) #FOS: Electrical engineering #Feasible region #Mathematical analysis #Mathematical optimization #Mathematics #Perturbation (astronomy) #Physics #Polynomial #Robotic Path Planning Algorithms #Robustness (evolution) #Sequence (biology) #Set (abstract data type) #State (computer science) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1812.10588
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2018/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.