Seyed Mehdi Mirhosseini-Alizamini - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran

‎The controlled harmonic oscillator with retarded damping‎, ‎is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems‎. ‎In this paper‎, ‎to solve this problem‎, ‎we presented an analytical method‎. ‎This approach is based on the homotopy perturbation method‎. ‎The solution procedure becomes easier‎, ‎simpler and more straightforward‎. ‎In order to use the proposed method‎, ‎a control design algorithm with low computational complexity is presented‎. ‎Through the finite iterations of the proposed algorithm‎, ‎a suboptimal control law is obtained for the problems‎. ‎Finally‎, ‎the obtained results have been compared with the exact solution of the controlled harmonic oscillator and variational iteration method‎, ‎so that the high accuracy of the results is clear.

Suboptimal control‎, ‎Harmonic oscillator‎, ‎Damping‎, ‎Homotopy perturbation method