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Optimal preview control for a class of continuous time‐invariant descriptor systems
Author(s) -
Zhao Lei,
Sun FuQuan,
Ren JunChao,
Li BenWen
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.2166
Subject(s) - algebraic riccati equation , riccati equation , mathematics , linear quadratic regulator , optimal control , control theory (sociology) , invariant (physics) , differential equation , quadratic equation , lyapunov function , differential (mechanical device) , sequence (biology) , mathematical optimization , computer science , mathematical analysis , nonlinear system , control (management) , aerospace engineering , physics , geometry , quantum mechanics , artificial intelligence , biology , engineering , mathematical physics , genetics
Summary This paper presents the optimal finite horizon linear‐quadratic control for a class of continuous linear time‐invariant descriptor systems subject to a previewable desired output. For a quadratic performance index and a giving reference sequence, the solution is obtained in four steps. First, the continuous‐time descriptor systems with previewable desired tracking signals are transformed into augmented error descriptor systems. Then, the necessary optimality conditions are derived from the maximum principle. Finally, the necessary optimality conditions can be transformed into differential Riccati equation by performing singular value decomposition of E z . Subsequently, the solution of the differential Riccati equation can be obtained by solving the algebraic Riccati equation and the differential Lyapunov equation. The effectiveness and validity of the proposed approach have been demonstrated by an example. Copyright © 2015 John Wiley & Sons, Ltd.