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

Abstract : 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 Faà 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.
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https://hal.inria.fr/hal-02146572
Contributor : Nicolás Espitia <>
Submitted on : Tuesday, June 4, 2019 - 10:01:26 AM
Last modification on : Friday, December 11, 2020 - 6:44:07 PM

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Nicolás Espitia, Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti. Some characterizations of boundary time-varying feedbacks for fixed-time stabilization of reaction-diffusion systems. CPDE'19 - 3rd IFAC/IEEE CSS Workshop on Control of Systems Governed by Partial Differential Equations, May 2019, Oaxaca, Mexico. ⟨hal-02146572⟩

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