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

03/21/2018
by   Weiqiao Han, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset