Single-Step Optimal Design for a Class of Nonlinear Singular System and Epidemic Control

Abstract

The present research work proposes a method of optimal control for a class of nonlinear singular system, which applies single-step design, Zubov’s method and optimal control theory. Firstly, it makes the nonlinear singular system normalizable, realizes feedback linearization and the pole placement in a single step. Then, it constructs a performance index that is calculated explicitly as an algebraic function of the controller parameters by solving Zubov’s partial differential equation. Lastly, standard optimization techniques are employed for the calculation of the optimal values of the adjustable parameters. So we obtain the single-step optimal design of normalizability , feedback linearization with the pole placement for nonlinear singular system. The proposed approach is finally applied in a SIS model with logistic growth. The simulation result shows the feasibility and the effectiveness of the proposed method.