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arXiv · 1803.07725

Semidefinite Outer Approximation of the Backward Reachable Set of Discrete-time Autonomous Polynomial Systems

Weiqiao Han·Russ Tedrake
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Abstract

We approximate the backward reachable set of discrete-time autonomous polynomial systems using the recently developed occupation measure approach. We formulate the problem as an infinite-dimensional linear programming (LP) problem on measures and its dual on continuous functions. Then we approximate the LP by a hierarchy of finite-dimensional semidefinite programming (SDP) programs on moments of measures and their duals on sums-of-squares polynomials. Finally we solve the SDP's and obtain a sequence of outer approximations of the backward reachable set. We demonstrate our approach on three dynamical systems. As a special case, we also show how to approximate the preimage of a compact semi-algebraic set under a polynomial map.

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Weiqiao Han, Russ Tedrake. 2018-03-21. Semidefinite Outer Approximation of the Backward Reachable Set of Discrete-time Autonomous Polynomial Systems. https://arxiv.org/abs/1803.07725

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