Numerical Solution of the Controlled Harmonic Oscillator by Homotopy Perturbation Method

ýThe controlled harmonic oscillator with retarded dampingý, ýis an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systemsý. ýIn this paperý, ýto solve this problemý, ýwe presented an analytical methodý. ýThis approach is based on the homotopy perturbation methodý. ýThe solution procedure becomes easierý, ýsimpler and more straightforwardý. ýIn order to use the proposed methodý, ýa control design algorithm with low computational complexity is presentedý. ýThrough the finite iterations of the proposed algorithmý, ýa suboptimal control law is obtained for the problemsý. ýFinallyý, ýthe obtained results have been compared with the exact solution of the controlled harmonic oscillator and variational iteration methodý, ýso that the high accuracy of the results is clear.