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Alternative Method of Solution of the Regulator Equation: L 2 ‐Space Approach
Author(s) -
Rehák B.
Publication year - 2012
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.416
Subject(s) - mathematics , banach space , nonlinear system , regulator , partial differential equation , contraction (grammar) , contraction mapping , first order partial differential equation , mathematical analysis , sequence (biology) , differential equation , fixed point theorem , physics , medicine , biochemistry , chemistry , genetics , quantum mechanics , biology , gene
Abstract An alternative method for the proof of solvability of the differential equation that is a part of the regulator equation which arises from the solution of the output regulation problem. The proof uses the L 2 ‐space based theory of solutions of partial differential equations for the case of the linear output regulation problem. In the nonlinear case, a sequence of linear equations is defined so that their solutions converge to the solution of the nonlinear problem. This is proved using the Banach Contraction Theorem. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society