占有測度による非線形フィードバック制御器の凸最適化
Technical Report: Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures
多項式システムに対し、時間制限付き後方可到達集合を最大化するフィードバック制御器を、占有測度とSDP緩和を用いて凸最適化で設計する手法を提案した論文。
著者: Anirudha Majumdar, Ram Vasudevan, Mark M. Tobenkin, Russ Tedrake
分類: cs.RO, cs.SY, eess.SY, math.OC
原文アブストラクト
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.
