Using the Pontryagin’s maximum principle for a time-delayed optimal control problem results in a system of coupled two-point boundary-value problems (BVPs) involving both time-advance and time-delay arguments. The analytical solution of this advance-delay two-point BVP is extremely difficult, if not impossible. This paper provides a discrete general form of the numerical solution for the derived advance-delay system by applying a finite difference θ-method. This method is also implemented for the infinite-time horizon time-delayed optimal control problems by using a piecewise version of the θ-method. A matrix formulation and the error analysis of the suggested technique are provided. The new scheme is accurate, fast and very effective for the optimal control of linear and nonlinear time-delay systems. Various types of finite- and infinite-time horizon problems are included to demonstrate the accuracy, validity and applicability of the new technique.

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timeadvance error analysis advancedelay twopoint bvp technique timedelay piecewise version scheme analytical solution infinitetime horizon timedelayed optimal control problems general form finite difference italicitalicmethod pontryagins maximum principle optimal control of linear and nonlinear timedelay italicitalicmethod a matrix formulation coupled twopoint boundaryvalue problems

Amin Jajarmi,Mojtaba Hajipour,.Numerical solution of the state-delayed optimal control problems by a fast and accurate finite difference θ-method. 55 (0),.

Amin Jajarmi,Mojtaba Hajipour,"Numerical solution of the state-delayed optimal control problems by a fast and accurate finite difference θ-method" 55

Amin Jajarmi,Mojtaba Hajipour,"Numerical solution of the state-delayed optimal control problems by a fast and accurate finite difference θ-method"