Generating invariants of hybrid systems via sums-of-squares of polynomials with rational coefficients

Authors:
Min Wu;Zhengfeng Yang
Affiliations:
East China Normal University, Shanghai, China;East China Normal University, Shanghai, China
Venue:
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Year:
2012

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Abstract

In this paper we discuss how to generate inequality invariants for continuous dynamical systems involved in hybrid systems. A hybrid symbolic-numeric algorithm is presented to compute inequality invariants of the given systems, by transforming this problem into a parameterized polynomial optimization problem. A numerical inequality invariant of the given system can be obtained by applying polynomial Sum-of-Squares (SOS) relaxation via Semidefinite Programming (SDP). And a method based on Gauss-Newton refinement is deployed to obtain candidates of polynomials with rational coefficients, and finally we certify that this polynomial exactly satisfies the conditions of invariants, by use of SOS representation of polynomials with rational coefficients. Several examples are given to show that our algorithm can successfully yield inequality invariants with rational coefficients.