Polynomial Controller Synthesis of Nonlinear Systems with Continuous State Feedback Using Trust Regions

We present a novel, correct-by-construction control approach for disturbed, nonlinear systems with continuous state feedback under state and input constraints. For the first time, we jointly synthesize a feedforward and feedback controller by solving a single non-convex, continuously differentiable approximation of the original synthesis problem, which we combine with a trust-region approach in an iterative manner to obtain non-conservative results. We ensure the formal correctness of our algorithm through reachability analysis and show that its computational complexity is polynomial in the state dimension for each trust-region iteration. In contrast to previous work, we also avoid the introduction of several algorithm parameters that require expert knowledge to tune, making the proposed synthesis approach easier to use for non-experts while guaranteeing state and input constraint satisfaction. Numerical benchmarks demonstrate the applicability of our novel synthesis approach.