Some characterizations of boundary time-varying feedbacks for fixed-time stabilization of reaction-diffusion systems

被引：9

作者：

Espitia, Nicolas ^{[1
]}

Polyakov, Andrey ^{[1
]}

Efimov, Denis ^{[1
]}

Perruquetti, Wilfrid ^{[2
]}

机构：

[1] INRIA, Lille Nord Europe, Parc Sci Haute Borne,40 AyHalley, F-59650 Villeneuve Dascq, France

[2] Ecole Cent Lille, CRIStAL UMR CNRS 9189, BP 48, F-59651 Villeneuve Dascq, France

来源：

IFAC PAPERSONLINE | 2019年 / 52卷 / 02期

关键词：

Reaction-diffusion equations; time-varying feedbacks; fixed-time convergence; exponential Bell polynomials; generalized Laguerre polynomials; FINITE-TIME; EQUATIONS; NUMBERS; DESIGN; SPACE; HEAT;

D O I：

10.1016/j.ifacol.2019.08.029

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper deals with continuous boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction-diffusion systems. The time of convergence can be prescribed and is independent of the initial condition of the system. The design of time-varying feedbacks is carried out by using the backstepping approach for which suitable characterizations for time-varying kernels are derived. Kernel solutions are given in terms of power series involving the exponential complete Bell polynomials for which we have exploited the Faa di Bruno formula. Moreover, by particularizing the characterization, one can recover kernel solutions in terms of the generalized Laguerre polynomials and the modified Bessel functions. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

引用

页码：162 / 167

页数：6

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