Design of nonlinear continuous time predictive controller by solving the differential-algebraic equations with boundary conditions using homotopy perturbation method

In this paper, design of continuous time predictive controller and solving the resulting differential-algebraic equations are presented using the semi-analytical homotopy perturbation method. At any updating time of the continuous time predictive control algorithm, an optimal open loop control problem must be solved. In order to solve the predictive control problem in continuous time, the problem of optimal control is solved by an indirect method. For this purpose, the necessary and sufficient conditions for optimality are determined by applying the variational calculus and the Pontryagin's minimum principle. A system of differential-algebraic equations with boundary conditions is created. Homotopy perturbation method is proposed to semi-analytically solve this problem. By specifying the control and the state functions, we can obtain easily the control and the state values in every instance of the prediction horizon. The presented method can be used to design of continuous-time predictive controller of linear, nonlinear and time varying systems. To illustrate the reliability and efficiency of the proposed method, some numerical examples with simulation results are presented.