Prescribed-time Control for Linear Systems in Canonical Form Via Nonlinear Feedback

TL;DR

This paper introduces a nonlinear, time-varying feedback control method for linear systems in canonical form, achieving prescribed-time regulation despite uncertainties, and unifying linear and nonlinear control approaches.

Contribution

It presents a novel prescribed-time control scheme using a hyperbolic-tangent-like function and extends it to output feedback, bridging linear and nonlinear control methods.

Findings

Achieves prescribed-time regulation regardless of initial conditions.

Unifies linear and nonlinear feedback control within a single framework.

Ensures stability types including asymptotic, exponential, and prescribed-time.

Abstract

For systems in canonical form with nonvanishing uncertainties/disturbances, this work presents an approach to full state regulation within prescribed time irrespective of initial conditions. By introducing the smooth hyperbolic-tangent-like function, a nonlinear and time-varying state feedback control scheme is constructed, which is further extended to address output feedback based prescribed-time regulation by invoking the prescribed-time observer, all are applicable over the entire operational time zone. As an alternative to full state regulation within user-assignable time interval, the proposed method analytically bridges the divide between linear and nonlinear feedback based prescribed-time control, and is able to achieve asymptotic stability, exponential stability and prescribed-time stability with a unified control structure.