Prescribed-Time Control and Its Latest Developments

TL;DR

This paper provides a comprehensive survey of prescribed-time control, highlighting its ability to stabilize systems within a user-defined finite time and reviewing recent advancements across various system types and control strategies.

Contribution

It offers a structured taxonomy and synthesis of recent developments in prescribed-time control, including key techniques, assumptions, and future research directions.

Findings

PT control achieves system stability within a user-defined finite time.

Recent advancements include robust, adaptive, SISO, MIMO, and multi-agent system control.

The survey identifies key techniques and future research directions in PT control.

Abstract

Prescribed-time (PT) control, originated from \textit{Song et al.}, has gained increasing attention among control community. The salient feature of PT control lies in its ability to achieve system stability within a finite settling time user-assignable in advance irrespective of initial conditions. It is such a unique feature that has enticed many follow-up studies on this technically important area, motivating numerous research advancements. In this article, we provide a comprehensive survey on the recent developments in PT control. Through a concise introduction to the concept of PT control, and a unique taxonomy covering: 1) from robust PT control to adaptive PT control; 2) from PT control for single-input-single-output (SISO) systems to multi-input-multi-output (MIMO) systems; and 3) from PT control for single systems to multi-agent systems, we present an accessible review of this interesting topic. We highlight key techniques, fundamental assumptions adopted in various developments as well as some new design ideas. We also discuss several possibles future research directions towards PT control.