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In this paper, we present an approach for designing feedback controllers forpolynomial systems that maximize the size of the time-limited backwardsreachable set (BRS). We rely on the notion of occupation measures to pose thesynthesis problem as an infinite dimensional linear program (LP) and providefinite dimensional approximations of this LP in terms of semidefinite programs(SDPs). The solution to each SDP yields a polynomial control policy and anouter approximation of the largest achievable BRS. In contrast to traditionalLyapunov based approaches which are non-convex and require feasibleinitialization, our approach is convex and does not require any form ofinitialization. The resulting time-varying controllers and approximatedreachable sets are well-suited for use in a trajectory library or feedbackmotion planning algorithm. We demonstrate the efficacy and scalability of ourapproach on five nonlinear systems.

Technical Report: Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures