Discrete-time adaptive fuzzy control of continuous-time nonlinear systems

In this paper, we develop a discrete-time controller for continuous-time nonlinear plant. The exact dynamics of the plant are unknown, but some bounds of the dynamics are assumed. The controller consists of a supervisory controller and an adaptive fuzzy controller. The supervisory controller is designed to guarantee the boundedness of the state, and the adaptive fuzzy controller is designed to control the state to track a given trajectory. More specifically, the supervisory controller is constructed from the bounds of the plant dynamics in such a way that once the state moves outside the stable region, the supervisory controller will take action to draw it back. The adaptive fuzzy controller is constructed from the measured state and control data using the nearest neighborhood clustering algorithm. Both the supervisory controller and the adaptive fuzzy controller operate at discrete-time points, whereas the plant keeps running continuously. We give rigorous proofs of the properties of this sampled-data nonlinear adaptive control system