On the Solution Set of the Admissible Bounded Control Problem via Orthogonal Polynomials

Abstract

The complete set of solutions to the admissible bounded control problem of the Brunovsky control system of dimension $m$ for $m\geq 2$ via orthogonal polynomials on $[0,T]$ and their second kind polynomials is obtained. For $m\geq 2$ given an initial position $x_0$ and a time $T$ greater than the optimal time $t_{\min}$ , we prove that there are only two bang-bang controls with $m$ switchings that steer the state trajectory to the origin exactly at time $T$ .