Data-Driven Near Optimization for Fast Sampling Singularly Perturbed Systems

The optimal control issue of fast sampling singularly perturbed systems is discussed throughout this paper. As a new attempt, without using complete system dynamics, the composite controller is designed by using controller of the different subsystems along with the usage of the subsystem decomposition technique by means of singular perturbation theory. Compared with the existing policy iteration and value iteration algorithms, there is not an enforced requirement for a stabilizing control strategy and the increase in convergence speed is achieved by the proposed hybrid iteration algorithm. For the purpose of considering that the fast and slow subsystems have different characteristics, two hybrid iteration algorithms that can be applied in different situations are developed. Meanwhile, the difference between the given composite controller and the optimal controller is analyzed in detail. Finally, the validity of the proposed controller design method is demonstrated by an example.