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Keywords:

  • optimal control;
  • delay;
  • hybrid functions;
  • Chebyshev–Gauss–Lobatto points;
  • composite Chebyshev finite difference

SUMMARY

In this paper, a composite Chebyshev finite difference method is introduced and applied for finding the solution of optimal control of time-delay systems with a quadratic performance index. This method is an extension of the Chebyshev finite difference scheme. The proposed method can be regarded as a nonuniform finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev–Gauss–Lobatto points. Various types of time-delay systems are included to demonstrate the validity and the applicability of the technique. The method is easy to implement and provides very accurate results. Copyright © 2012 John Wiley & Sons, Ltd.