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Multi‐model LQ‐constrained min–max control
Author(s) -
García Pablo,
Poznyak Alexander
Publication year - 2015
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2173
Subject(s) - lagrange multiplier , mathematics , constraint (computer aided design) , quadratic equation , simple (philosophy) , optimal control , constraint algorithm , mathematical optimization , controller (irrigation) , control theory (sociology) , multiplier (economics) , variable (mathematics) , control (management) , computer science , mathematical analysis , agronomy , philosophy , geometry , epistemology , artificial intelligence , biology , macroeconomics , economics
Summary This paper deals with the designing of a min–max controller that provides the minimum value of maximal (among a finite number of linear models) quadratic functional under a simple constraint for a control amplitude. Using the Lagrange multipliers approach, we show that the consideration of this constraint implies the existence of a new adjoint variable (treated as a time‐varying Lagrange multiplier), providing the closed‐form solutions for the considered multi‐model LQ‐constrained min–max control problem. The method is illustrated by three numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.