Brief Control parametrization enhancing technique for optimal discrete-valued control problems

  • Authors:

  • H. W. J. Lee;K. L. Teo;V. Rehbock;L. S. Jennings

  • Affiliations:

  • Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;School of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, WA 6845, Australia;Department of Mathematics, The University of Western Australia, Nedlands, WA 6907, Australia

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1999

Quantified Score

Hi-index 22.15

Visualization

Abstract

In this paper, we consider a class of optimal discrete-valued control problems. Since the range set of the control function is a discrete set and hence not convex. These problems are, in fact, nonlinear combinatorial optimization problems. Using the novel idea of the control parametrization enhancing technique, it is shown that optimal discrete-valued control problems are equivalent to optimal control problems involving a new control function which is piecewise constant with pre-fixed switching points. The transformed problems are essentially optimal parameter selection problems and can hence be readily solved by various existing algorithms. A practical numerical example is solved using the proposed method.