Some controls applications of sum of squares programming

We consider nonlinear systems with polynomial vector fields and present two algorithms based on sum of squares programming, that may answer system theoretic questions. The first algorithm provides a bound for the reachable set of a system driven by a unit-energy disturbance, while the second synthesizes a polynomial state feedback controller to enlarge the provable region of attraction. We also outline a variant of the second algorithm for handling systems with input saturation. Both algorithms are demonstrated using two-state nonlinear systems.