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Gradient-flow approach for computing a nonlinear-quadratic optimal-output feedback gain matrix

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Abstract

In this paper, an approach is proposed for solving a nonlinear-quadratic optimal regulator problem with linear static state feedback and infinite planning horizon. For such a problem, approximate problems are introduced and considered, which are obtained by combining a finite-horizon problem with an infinite-horizon linear problem in a certain way. A gradient-flow based algorithm is derived for these approximate problems. It is shown that an optimal solution to the original problem can be found as the limit of a sequence of solutions to the approximate problems. Several important properties are obtained. For illustration, two numerical examples are presented.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Western Australia, Nedlands, Western Australia, Australia

    K. L. Teo (Associate Professor)

  2. Department of Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa

    K. H. Wong (Senior Lecturer)

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Republic of Singapore

    W. Y. Yan (LKY Fellow)

Authors
  1. K. L. Teo
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  2. K. H. Wong
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  3. W. Y. Yan
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Additional information

Communicated by T. L. Vincent

This project was partially supported by a research grant from the Australian Research Council.

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Teo, K.L., Wong, K.H. & Yan, W.Y. Gradient-flow approach for computing a nonlinear-quadratic optimal-output feedback gain matrix. J Optim Theory Appl 85, 75–96 (1995). https://doi.org/10.1007/BF02192300

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