A numerical solution to the minimum-time control problem for linear discrete-time systems
Abstract
The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging problem in optimal control theory for which closed-form solutions exist only for a few systems of small dimensions. This paper presents a very generic solution to the minimum-time problem for arbitrary discrete-time linear systems. It is a numerical solution based on sparse optimization, that is the minimization of the number of nonzero elements in the state sequence over a fixed control horizon. We consider both single input and multiple inputs systems. An important observation is that, contrary to the continuous-time case, the minimum-time control for discrete-time systems is not necessarily entirely bang-bang.
Cite
@article{arxiv.1109.3772,
title = {A numerical solution to the minimum-time control problem for linear discrete-time systems},
author = {Laurent Bako and Dulin Chen and Stéphane Lecoeuche},
journal= {arXiv preprint arXiv:1109.3772},
year = {2015}
}