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Robust Control System Design for an Uncertain Nonlinear System Using Minimax LQG Design Method
Author(s) -
Ur Rehman Obaid,
Fidan Bariş,
Petersen Ian R.
Publication year - 2014
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.777
Subject(s) - control theory (sociology) , linear quadratic gaussian control , optimal projection equations , feedback linearization , minimax , nonlinear system , robust control , linear quadratic regulator , linearization , controller (irrigation) , optimal control , mathematics , computer science , mathematical optimization , control (management) , physics , quantum mechanics , artificial intelligence , agronomy , biology
A systematic approach to design a nonlinear controller using minimax linear quadratic Gaussian regulator ( LQG ) control is proposed for a class of multi‐input multi‐output nonlinear uncertain systems. In this approach, a robust feedback linearization method and a notion of uncertain diffeomorphism are used to obtain an uncertain linearized model for the corresponding uncertain nonlinear system. A robust minimax LQG controller is then proposed for reference command tracking and stabilization of the nonlinear system in the presence of uncertain parameters. The uncertainties are assumed to satisfy a certain integral quadratic constraint condition. In this method, conventional feedback linearization is used to cancel nominal nonlinear terms and the uncertain nonlinear terms are linearized in a robust way. To demonstrate the effectiveness of the proposed approach, a minimax LQG ‐based robust controller is designed for a nonlinear uncertain model of an air‐breathing hypersonic flight vehicle ( AHFV ) with flexibility and input coupling. Here, the problem of constructing a guaranteed cost controller which minimizes a guaranteed cost bound has been considered and the tracking of velocity and altitude is achieved under inertial and aerodynamic uncertainties.