On analysis and synthesis of safe control laws

Controller synthesis for nonlinear systems is considered with the following ob-jective: no trajectory starting from a given set of initial states is allowed to enter into a given set of forbidden (unsafe) states. A methodology for safety verification using barrier certificates has recently been proposed. Here it is shown how a safe control law together with a corresponding certificate can be computed by means of convex optimization. A basic tool is the theory for density functions in analysis of nonlinear systems. Computational examples are considered.