Parameter estimation of optimal control problems based on game theory and tracking method

Optimal control theory has been widely used in many fields such as engineering, economics, and science. However, in many practical problems, some parameters in the system model are usually unknown, and the accurate estimation of these unknown parameters is crucial for solving optimal control problems. Therefore, this paper proposes a new parameter estimation method based on game theory and tracking method (called GTM), which firstly transforms the optimal control problem into a differential game problem by introducing a perturbation term, and then estimates the parameters of the optimal control problem. By this method, we can estimate the optimal control function and the parameter estimates simultaneously. At the same time, we also show that the estimator is consistently convergent and achieves the root n-rate. In the numerical simulation part, this paper verifies the robustness and accuracy of the method in parameter estimation by comparing it with the nonlinear least squares method and the maximum likelihood method. Finally, empirical analyses were conducted to estimate the time-varying parameters of the SIRD model using data related to COVID-19 in the state of Amazonas, Brazil, as an example, to verify the effectiveness of GTM. Meanwhile, predictions were made based on data from the early stages of the epidemic, and the experimental results showed that GTM has high accuracy.