Computing an invariance kernel with target by computing Lyapunov‐like functions

Reachability analysis and viability theory play an important role in control synthesis and trajectory analysis of constrained dynamical systems, many methods are known for computing them in low‐dimensional non‐linear systems, but these well‐known methods rely on gridding the state space and hence suffer from the curse of dimensionality. In this study, for systems whose dynamics are described by polynomials, a method based on semi‐definite programming is proposed to estimate an invariance kernel with target as large as possible by iteratively searching for Lyapunov‐like functions. The proposed methodology is scalable, since the size of the semi‐definite programming problem to be solved grows linearly with the system dimension. We test the method on two interesting examples and compare them with some existing methods, the results show that our method is more efficient.