Minimal controllability time for systems with nonlinear drift under a compact convex state constraint

TL;DR

This paper estimates the minimal controllability time for nonlinear control systems with convex state constraints, providing explicit formulas and bounds, and analyzing control strategies through lower-dimensional systems.

Contribution

It introduces a method to compute or bound the minimal controllability time for nonlinear systems with convex constraints, including explicit solutions when the control matrix has co-dimension one.

Findings

Explicit expression for controllability time when control matrix has co-dimension one

Lower bounds for controllability time in general cases

Analytical computation of controls near minimal time

Abstract

In this paper we estimate the minimal controllability time for a class of non-linear control systems with a bounded convex state constraint. An explicit expression is given for the controllability time if the image of the control matrix is of co-dimension one. A lower bound for the controllability time is given in the general case. The technique is based on finding a lower dimension system with the similar controllability properties as the original system. The controls corresponding to the minimal time, or time close to the minimal one, are discussed and computed analytically. The effectiveness of the proposed approach is illustrated by a few examples.