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Optimization of Output Feedback Control Under Set-Membership Uncertainty

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Abstract

This paper presents a description of solution approaches to the problem of output feedback control under unknown but bounded disturbances with hard bounds on the controls and the uncertain items. The problem is treated within a finite horizon which requires to track the system dynamics throughout the whole time interval rather than through asymptotic properties. The demand for such solutions is motivated by increasing number of applications. The suggested approaches are designed as a combination of Hamiltonian techniques in the form of generalized dynamic programming with those of set-valued analysis and problems on minimax. The paper indicates the crucial role of properly selecting the on-line generalized state of the system in the form of information states or information sets. The description ranges from theoretical schemes to computational routes with emphasis on the possibility of treating the overall problem through only finite-dimensional methods. The results apply to nonlinear systems, with more details for linear models. It turns out that in the last case, while moving through calculations, one may avoid the fairly difficult stage of integrating HJB equations. The procedures are here confined to ordinary differential equations and ellipsoidal or polyhedral techniques. The suggested schemes are also quite appropriate for parallel computation.

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State (Lomonosov) University, Moscow, 119991, Russia

    A. B. Kurzhanski

  2. Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, CA, 94720-1770, USA

    A. B. Kurzhanski & P. Varaiya

Authors
  1. A. B. Kurzhanski
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  2. P. Varaiya
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Correspondence to A. B. Kurzhanski.

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Communicated by G. Leitmann.

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Kurzhanski, A.B., Varaiya, P. Optimization of Output Feedback Control Under Set-Membership Uncertainty. J Optim Theory Appl 151, 11–32 (2011). https://doi.org/10.1007/s10957-011-9861-z

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