離散時間多項式システムの後方到達可能集合の半正定値外近似
Semidefinite Outer Approximation of the Backward Reachable Set of Discrete-time Autonomous Polynomial Systems
占有測度アプローチを用いて離散時間自律多項式システムの後方到達可能集合を無限次元線形計画問題として定式化し、モーメント上の半正定値計画の階層で外側近似を求める手法を提案した。
著者: Weiqiao Han, Russ Tedrake
分類: eess.SY, cs.RO, cs.SY, math.OC
原文アブストラクト
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.
