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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 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.
We address the problem of designing optimal linear time-invariant (LTI) sparse controllers for LTI systems, which corresponds to minimizing a norm of the closed-loop system subject to sparsity constraints on the controller structure. This problem is
This paper presents a provably correct method for robot navigation in 2D environments cluttered with familiar but unexpected non-convex, star-shaped obstacles as well as completely unknown, convex obstacles. We presuppose a limited range onboard sens
We propose a convex optimization procedure for black-box identification of nonlinear state-space models for systems that exhibit stable limit cycles (unforced periodic solutions). It extends the robust identification error framework in which a convex
This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small set of repe
In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable for state