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In this research, we present an expanded hp-method for solving time delay optimal control (TDOC) problems, applicable to issues with both smooth and nonsmooth solutions. The method discretizes the time domain using an adaptive grid with unknown switch points. Subsequently, we use the operational integration matrix to approximate the problem’s state variable derivative. Next, we approximate the state and control variables using the Legendre–Gauss–Lobatto points and Legendre spectral collocation. This formulation transforms the original problem into a nonlinear programming problem, solvable using relevant techniques. To demonstrate the efficacy of the proposed method, we solve numerical examples and compare the obtained results with those of several exiting methods. |
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