Assessment of He's homotopy perturbation method for optimal control of linear time-delay systems

This paper renders an optimal regulator for a system with state time-delayand quadratic performance index. First, by means of Maximum Principle andnecessary optimal conditions, a continues-time two-point boundary-value problem(TPBVP) including both time-delay and time-advance is derived. Then, usingHomotopy Perturbation Method (HPM), the obtained TPBVP is transformed intoa sequence of linear time-invariant TPBVP without any time-delay or timeadvance.Solving the resulted linear TPBVP sequence in a recursive manner,concludes that the optimal control law in the form of rapid convergent series. Atthe end, an iterative algorithm with low complexity in computation and fastconvergence rate is proposed to achieve an accurate enough suboptimal controllaw. It's worth noting that simulation based on application of a harmonicoscillator is conducted to demonstrate efficiency of this method.