2010/12/06 by Mohamed Amin Ben Sassi, Antoine Girard, Sassi, Mohamed Amin Ben +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Formal Methods in Verification #Lipid metabolism and biosynthesis #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1012.1256
openalex publication_date 2010/12/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
This paper deals with the computation of polytopic invariant sets for\npolynomial dynamical systems. An invariant set of a dynamical system is a\nsubset of the state space such that if the state of the system belongs to the\nset at a given instant, it will remain in the set forever in the future.\nPolytopic invariants for polynomial systems can be verified by solving a set of\noptimization problems involving multivariate polynomials on bounded polytopes.\nUsing the blossoming principle together with properties of multi-affine\nfunctions on rectangles and Lagrangian duality, we show that certified lower\nbounds of the optimal values of such optimization problems can be computed\neffectively using linear programs. This allows us to propose a method based on\nlinear programming for verifying polytopic invariant sets of polynomial\ndynamical systems. Additionally, using sensitivity analysis of linear programs,\none can iteratively compute a polytopic invariant set. Finally, we show using a\nset of examples borrowed from biological applications, that our approach is\neffective in practice.\n