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We consider nonlinear systems with polynomial vector fields and pose two classes of system theoretic problems that may be solved by sum of squares programming. The first is disturbance analysis using three different norms to bound the reachable set. The second is the synthesis of a polynomial state feedback controller to enlarge the provable region of attraction. We also outline a variant...
We present an approach to uncertainty propagation in dynamic systems, exploiting information provided by related experimental results along with their models. The approach relies on a solution mapping technique to approximate mathematical models by polynomial surrogate models. We use these surrogate models to formulate prediction bounds in terms of polynomial optimizations. Recent results on polynomial...
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