2016/05/04 by Hui Kong, Sergiy Bogomolov, Kong, Hui +7
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Polynomial and algebraic computation #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1605.01450
openalex publication_date 2016/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we propose an approach to automatically compute invariant clusters for semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u,x)=0, parametric in u, which can yield an infinite number of concrete invariants by assigning different values to u so that every trajectory of the system can be overapproximated precisely by a union of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial vector flow, invariant clusters can be obtained by first computing the remainder of the Lie derivative of a template multivariate polynomial w.r.t. its Groebner basis and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is effective and efficient.