Observer based adaptive control of nonlinear systems using filtered-FNN design

In this paper, we consider the observer based adaptive control design problem for output tracking of nonlinear systems. As we assume that the states are not measurable, a state error observer is introduced to design the adaptive controller. Based on a derived error model, a filtered fuzzy neural network using estimated states as network input is applied to design the main component of the adaptive controller. In order to compensate for the uncertainties from the network approximation error and unknown input gain, we use a normalization signal to construct a bounding function as a robust control term. Finally, an averaging filter is proposed to solve the design issue of relative degree problem. We show by a Lyapunov analysis that all the adjustable parameters as well as internal signals in the closed loop system remain bounded. Furthermore, the norm of output tracking error will asymptotically converge to a tunable residual set as time goes to infinity. Finally, we discuss the extension of the proposed design to an iterative learning control issue for nonlinear systems without state measurement.