On Analysis and Synthesis of Safe Control Laws

Controller synthesis for nonlinear systems is considered with the following objective: 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 barrier certificate can be computated by means of convex optimization. A basic tool is thetheory for density functions in analysis of nonlinear systems.Computational examples are considered