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A new approach to constrained state estimation for discrete‐time linear systems with unknown inputs
Author(s) -
Garcia Tirado Jose Fernando,
MarquezRuiz Alejandro,
Botero Castro Hector,
Angulo Fabiola
Publication year - 2017
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.3874
Subject(s) - minimax , estimator , mathematical optimization , constraint (computer aided design) , filter (signal processing) , optimization problem , control theory (sociology) , computer science , minimax estimator , constructive , mathematics , control (management) , process (computing) , minimum variance unbiased estimator , statistics , geometry , artificial intelligence , computer vision , operating system
Summary This paper addresses the problem of estimating the state for a class of uncertain discrete‐time linear systems with constraints by using an optimization‐based approach. The proposed scheme uses the moving horizon estimation philosophy together with the game theoretical approach to the H ∞ filtering to obtain a robust filter with constraint handling. The used approach is constructive since the proposed moving horizon estimator (MHE) results from an approximation of a type of full information estimator for uncertain discrete‐time linear systems, named in short H ∞ ‐MHE and H ∞ –full information estimator, respectively. Sufficient conditions for the stability of the H ∞ ‐MHE are discussed for a class of uncertain discrete‐time linear systems with constraints. Finally, since the H ∞ ‐MHE needs the solution of a complex minimax optimization problem at each sampling time, we propose an approximation to relax the optimization problem and hence to obtain a feasible numerical solution of the proposed filter. Simulation results show the effectiveness of the robust filter proposed.