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

Abstract : In this paper, the problem of fixed-time stabilization of constant-parameter reaction-diffusion partial differential equations by means of continuous boundary time-varying feedbacks is considered. Moreover, the time of convergence can be prescribed in the design. The design of time-varying feedbacks is carried out based on the backstepping approach. Using a suitable target system with a time varying-coefficient, one can state that the resulting kernel of the backstepping transformation is time-varying and rendering the control feedback to be time-varying as well. Explicit representations of the kernel solution in terms of generalized Laguerre polynomials and modified Bessel functions are derived. The fixed-time stability property is then proved. A simulation example is presented to illustrate the main results.
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Submitted on : Thursday, December 20, 2018 - 5:20:21 PM
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Nicolás Espitia, Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti. Boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction-diffusion systems. Automatica, Elsevier, 2019, 103, pp.398-407. ⟨10.1016/j.automatica.2019.02.013⟩. ⟨hal-01962662⟩

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