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We consider the problem of ensuring the safety of nonlinear control systemsunder adversarial signals. Using Lyapunov based reachability analysis, we firstgive sufficient conditions to assess safety, i.e., to guarantee that the statesof the control system, when starting from a given initial set, always remain ina prescribed safe set. We consider polynomial systems with semi-algebraic safesets. Using the S-procedure for polynomial functions, safety conditions can beformulated as a Sum-Of-Squares (SOS) programme, which can be solvedefficiently. When safety cannot be guaranteed, we provide tools via SOS tosynthesize polynomial controllers that enforce safety of the closed loopsystem. The theoretical results are illustrated through numerical simulations.

Secondary Controller Design for the Safety of Nonlinear Systems via Sum-of-Squares Programming