Prescribed-Time Regulation of Nonlinear Uncertain Systems with Unknown Input Gain and Appended Dynamics

TL;DR

This paper develops a control method for nonlinear uncertain systems that guarantees finite-time convergence to the origin, regardless of initial conditions, even with unknown input gain and appended dynamics.

Contribution

It introduces a novel prescribed-time stabilization approach for complex nonlinear systems with uncertainties and unmeasured states, using a combination of time scale transformation and adaptive control.

Findings

Achieves finite-time stabilization with arbitrary prescribed convergence time.

Handles systems with unknown input gain and appended dynamics.

Demonstrates effectiveness through theoretical analysis and simulations.

Abstract

The prescribed-time stabilization problem for a general class of nonlinear systems with unknown input gain and appended dynamics (with unmeasured state) is addressed. Unlike the asymptotic stabilization problem, the prescribed-time stabilization objective requires convergence of the state to the origin in a finite time that can be arbitrarily picked (i.e., prescribed) by the control system designer irrespective of the initial condition of the system. The class of systems considered is allowed to have general nonlinear uncertain terms throughout the system dynamics as well as uncertain appended dynamics (that effectively generate a time-varying non-vanishing disturbance signal input into the nominal system). The control design is based on a time scale transformation, dynamic high-gain scaling, and adaptation dynamics with temporal forcing terms.