Secondary Controller Design for the Safety of Nonlinear Systems via Sum-of-Squares Programming
Yankai Lin, M. S. Chong, Carlos Murguia · 2023
We consider the problem of ensuring the safety of nonlinear control systems under adversarial signals. Using Lyapunov-based reachability analysis, we first give sufficient conditions to assess safety, i.e., to guarantee that the states of the control system, when starting from a given initial set, always remain in a prescribed safe set. We consider polynomial systems with semi-algebraic safe sets. Using the S-procedure for polynomial functions, safety conditions can be formulated as a Sum-Of-Squares (SOS) programme, which can be solved efficiently. When safety cannot be guaranteed, we provide tools via SOS to synthesize polynomial controllers that enforce safety of the closed-loop system. The theoretical results are illustrated through numerical simulations.