On Boundary Finite-Time Feedback Control for Heat Equation

Abstract

The paper deals with boundary finite-time control for heat system. A linear switching control with state dependent switchings is designed based on backstepping procedure. It steers any solution of the heat system to zero in a finite time. The theoretical results are supported by numerical simulations.

Boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction–diffusion systems

“…In [23] for instance, by following some slidingmode techniques, a distributed power-fractional control strategy is used to stabilize an unperturbed heat equation in finite-time. In [25], a piecewise linear boundary control with a state dependent switching law is designed to boost the convergence of the state of the heat equation to zero in finite-time. The latter is highly inspired by [7] where the null controllability and finite-time sta-bilization of the heat equation are deeply studied.…”

“…This paper is then devoted to the fixed-time stabilization of a scalar reaction-diffusion system. Highly inspired by [7,25] and [29], we propose continuous boundary time-varying feedbacks for finite-time stabilization in a prescribed time; often refereed in this paper as fixedtime stabilization. The concept of fixed-time differs from finite-time whenever the settling time is independent of the initial condition as it is in our study.…”

“…A suitable target system, with a time-dependent coefficient is employed to come up with the time-varying kernel. It makes our approach considerably different w.r.t for example [25]. We provide an explicit representation of the kernel solution which involves a suitable dynamic variable whose solution blows up in prescribed finite-time.…”

Characterization of Finite/Fixed-time Stability of Evolution Inclusions

“…Finite/fixed-time control algorithms allows us to fulfill some time constrains [10]. Finite-time stable of infinite dimensional systems are studied, for example, in [11], [12], [13], [14].…”

On continuous boundary time-varying feedbacks for fixed-time stabilization of coupled reaction-diffusion systems

“…This paper considers the problem of fixed-time stabilization of coupled reaction-diffusion systems. Highly inspired by [6], [18], [2] and [16], we propose continuous boundary time-varying feedbacks for finite-time stabilization in a prescribed time. Actually, this work borrows the idea of prescribed time from [23] (for normal-form nonlinear systems) by using time-varying feedbacks subject to scaling of the states with blowing up functions.…”