Asymptotic Stabilization of Nonlinear Systems with Convex-Polytope Input Constraints and its Inverse Optimality * * This work is partially supported by JSPS KAKENHI Grant Number 16H04380.

摘要

In this study, we propose an asymptotic stabilization controller for a nonlinear system with a convex-polytope input constraint. Moreover, we establish a condition that the controller has inverse optimality in the neighborhood of the origin. The controller input is continuous in the set where the asymptotic stabilization is guaranteed. We consider the asymmetric constraint for zero-input, and this bias is adjusted by using an un-uniform scaling on each vertex point, in the neighborhood of the origin. Therefore, the input cost in the inverse optimal performance functional is approximated by a quadratic form near the origin.