Robust Control of Nonlinear Systems Using the Approach of Iterative Approximations

This paper presents a new approach to design a controller for nonlinear systems using the iterative approximation method. In the proposed approach, the nonlinear system is first approximated by several linear time-varying systems. Then, for each of the linear systems, a control law is designed and the calculated control law for the last system is applied to the nonlinear system. This paper shows that the conventional method in the iterative approximations is practically open-loop and becomes unstable after a short time. Then, the maximum duration of the stability in conventional controllers called T is evaluated using simulations in the case of a robot arm. In this paper, to establish a relationship between the controller and the nonlinear system, the process of approximation and design of the controller is repeated every T seconds. In this way, the control system is closed-loop, and every T second, using the updated feedback signal form the nonlinear system the control signal is updated. Finally, the efficiency of the proposed method is shown through a simulation.