On Averaging of a Class of "Non-Singularly Perturbed" Control Systems

TL;DR

This paper investigates control systems with variables changing at different rates, showing that slow trajectories approximate solutions of a differential inclusion, with implications for optimal control strategies.

Contribution

It introduces a novel analysis of non-singularly perturbed control systems, demonstrating the density of slow trajectories in solution sets and exploring their impact on optimal control.

Findings

Slow trajectories are dense in the solution set of a differential inclusion.

The results have implications for designing optimal control strategies.

The study extends understanding of systems with variables of different change rates.

Abstract

We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are dense in the set of solutions of a certain differential inclusion and discuss an implication of this result for optimal control.