Open AccessStable invariant manifolds with application to control problems
Author(s) -
Alexey V. Gorshkov
Publication year - 2022
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021040
Subject(s) - invariant (physics) , mathematics , linear subspace , invariant manifold , invariant subspace , invariant polynomial , center manifold , manifold (fluid mechanics) , pure mathematics , mathematical analysis , mathematical physics , nonlinear system , physics , mechanical engineering , hopf bifurcation , matrix polynomial , quantum mechanics , bifurcation , polynomial , engineering
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.