Abstract: This article presents a method of optimizing dynamic systems governed by integro-differential equations of the second kind with weakly singular kernels in such systems, the time range is infinite and the controls may be delayed. Performance assessments involve measuring the square distance between tracking functions and states and measuring the energy of controls, and measuring the deviation of the final states from the tracking functions. We report the results of typical examples.

Keywords: Integro-differential equations, Weakly singular, Tracking functions, Optimal controls.

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