Stable invariant manifolds with application to control problems

Alexey Gorshkov

doi:10.3934/mcrf.2021040

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2022, Volume 12, Issue 3: 695-707. Doi: 10.3934/mcrf.2021040

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Stable invariant manifolds with application to control problems

Alexey Gorshkov^,

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Russia, 119991, Moscow, GSP-1, 1 Leninskiye Gory, Main Building, Russia

^* Corresponding author: Alexey Gorshkov
^* Corresponding author: Alexey Gorshkov

Received: April 30, 2019

Revised: July 31, 2020

Early access: September 2021

Published: July 2022

This article was recruited by Andrii Mironchenko

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Abstract

In this article we develop the theory of stable invariant manifolds for evolution equations with application to control problem. We will construct invariant subspaces for linear equations which can be extended to the non-linear equations in the neighbourhood of the equilibrium with help of perturbation theory. Here will be considered both cases of the discrete and continuous spectrum of the generator associated with resolving semi-group. The example of global invariant manifold will be presented for Burgers equation.

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Mathematics Subject Classification: Primary: 37D10; Secondary: 93D15.

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