Semidefinite Outer Approximation of the Backward Reachable Set of Discrete-time Autonomous Polynomial Systems
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.
Keywords
Cite
@article{arxiv.1803.07725,
title = {Semidefinite Outer Approximation of the Backward Reachable Set of Discrete-time Autonomous Polynomial Systems},
author = {Weiqiao Han and Russ Tedrake},
journal= {arXiv preprint arXiv:1803.07725},
year = {2018}
}
Comments
merged with the paper arXiv:1803.09022