Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures
Author(s)Majumdar, Anirudha; Vasudevan, Ram; Tobenkin, Mark M.; Tedrake, Russell Louis
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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 backwards 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 four nonlinear systems.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of Robotics: Science and Systems IX
Majumdar, Anirudha, Ram Vasudevan, Mark M. Tobenkin, and Russ Tedrake. "Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures." Robotics: Science and Systems IX, 9.1 (June 2013).