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-delay and quadratic performance index. First, by means of Maximum Principle and necessary optimal conditions, a continues-time two-point boundary-value problem (TPBVP) including both time-delay and time-advance is derived. Then, using Homotopy Perturbation Method (HPM), the obtained TPBVP is transformed into a 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. At the end, an iterative algorithm with low complexity in computation and fast convergence rate is proposed to achieve an accurate enough suboptimal control law. It's worth noting that simulation based on application of a harmonic oscillator is conducted to demonstrate efficiency of this method.