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An SVD based strategy for receding horizon control of input constrained linear systems
Author(s) -
Rojas Osvaldo J.,
Goodwin Graham C.,
Serón María M.,
Feuer Arie
Publication year - 2004
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.940
Subject(s) - hessian matrix , singular value decomposition , model predictive control , mathematics , optimal control , control theory (sociology) , sequence (biology) , horizon , quadratic equation , mathematical optimization , singular value , basis (linear algebra) , computer science , control (management) , algorithm , artificial intelligence , eigenvalues and eigenvectors , physics , geometry , quantum mechanics , biology , genetics
A sub‐optimal receding horizon control strategy for input constrained linear systems is presented. The strategy is based on a singular value decomposition (SVD) of the Hessian of the quadratic performance index generally considered in model predictive control (MPC). The singular vectors are employed to generate a basis function expansion of the unconstrained solution to the finite horizon optimal control problem. At each sampling time, a feasible control sequence is determined by selecting a variable subset of the basis representation. No solution to the associated quadratic program is needed. For cases in which the Hessian is poorly conditioned, the proposed strategy can provide a sub‐optimal solution with minimal performance degradation. Properties of the singular values of the Hessian are also studied: it is shown that, for sufficiently long prediction horizons, the singular values are arbitrarily close to the magnitude of the energy density spectrum of the system seen by the performance index. Copyright © 2004 John Wiley & Sons, Ltd.