  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.
