Solving Time Series Optimization Problem Based on Nonlinear Equation

With the rapid development of science and technology, nonlinear equations and optimal control problems play an important role in a wide range of fields. However, in the current research, the method of solving nonlinear equations still has limitations. Firstly, the homotopy perturbation method, nonlinear equations and optimal control problems are briefly summarized. Then, the homotopy perturbation method and its convergence proof for the time series optimization problem of nonlinear equations are expounded, and the optimal control model studied in this paper is given. Finally, on the one hand, the equivalent homotopy perturbation method is used to solve the optimal control problems of three first-order linear systems and one second-order linear system. Through the above examples, it is proved that the nonlinear equation has less iterations, better convergence effect and more accurate approximate solution in the optimal control problem.