Technical Report: Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures
This provides a convex alternative to non-convex Lyapunov-based methods for feedback control in robotics or motion planning, though it appears incremental as it builds on occupation measures and SDP approximations.
The paper tackles the problem of designing feedback controllers for polynomial systems to maximize the size of time-limited backwards reachable sets, resulting in a convex method that avoids initialization and demonstrates efficacy on five nonlinear systems.
In this paper, we present an approach for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). We rely on the notion of occupation measures to pose the synthesis problem as an infinite dimensional linear program (LP) and provide finite dimensional approximations of this LP in terms of semidefinite programs (SDPs). The solution to each SDP yields a polynomial control policy and an outer approximation of the largest achievable BRS. In contrast to traditional Lyapunov based approaches which are non-convex and require feasible initialization, our approach is convex and does not require any form of initialization. The resulting time-varying controllers and approximated reachable sets are well-suited for use in a trajectory library or feedback motion planning algorithm. We demonstrate the efficacy and scalability of our approach on five nonlinear systems.