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Uniformly valid feedback expansions for optimal control of singularly perturbed dynamic systems

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Abstract

This paper shows how to construct a feedback control law for a class of singularly perturbed autonomous optimization problems. The control law is expressed as a single power series in the small parameter ∈ representing the ratio of the two effective time scales of the problem. The present approach avoids the need of expansion matching. The method is applied to a constant-speed interception problem. Comparison of numerical results with the exact solution shows an excellent agreement.

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Authors and Affiliations

  1. Department of Aeronautics and Astronautics, Stanford University, Stanford, California

    J. V. Breakwell (Professor)

  2. Department of Aeronautical Engineering, Technion, Israel Institute of Technology, Haifa, Israel

    J. Shinar (Professor)

  3. Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute, Blacksburg, Virginia

    H. G. Visser (Graduate Student)

Authors
  1. J. V. Breakwell
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  2. J. Shinar
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  3. H. G. Visser
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Dedicated to G. Leitmann

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Breakwell, J.V., Shinar, J. & Visser, H.G. Uniformly valid feedback expansions for optimal control of singularly perturbed dynamic systems. J Optim Theory Appl 46, 441–453 (1985). https://doi.org/10.1007/BF00939149

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  • DOI: https://doi.org/10.1007/BF00939149

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