New approach to the optimal control of delay systems via Chebyshev series

Based on the Chebyshev series, a directly computational formulation in matrix form is established for evaluating the optimal control and trajectory of time-delay systems. In a comparison with the previous work (3, Int. J. Control, Vol. 41, pp. 1221-1234, 1985), the formulation is shown to be more straightforward and convenient for digital computation. Thus the difficulty in obtaining a solution of the two-point boundary-value problem with both delayed and advanced arguments is circumvented. An example compares the actual solution with the one obtained using the technique of this paper.