Indirect Adaptive Control Based on the Recurrent Neurofuzzy Model

Abstract

The indirect adaptive regulation of unknown nonlinear dynamical systems with multiple inputs and states (MIMS) using F-RHONNs under the presence of parameter and dynamic uncertainties, is considered in this chapter. The method is based on the new NF dynamical systems definition introduced in Chap. 2, which uses the concept of adaptive fuzzy systems (AFS) operating in conjunction with recurrent high order neural networks. Since the plant is considered unknown, we first propose the calculation of fuzzy output centers by systems data or linguistic information and in the sequel the fuzzy rules are approximated by appropriate HONNs. Thus, the identification scheme leads up to fuzzy subsystems approximated by recurrent high order neural networks, which however takes into account the centers of the fuzzy output partitions (F-RHONNs). Every high order neural network approximates a group of fuzzy rules associated with each center. The indirect regulation is achieved by first identifying the system around the current operation point, and then using its parameters to device the control law. Weight updating laws for the involved HONNs are provided, which guarantee that, under the presence of both parameter and dynamic uncertainties, both the identification error and the system states reach zero, or at least uniform ultimate boundedness of all signals in the closed-loop. The control signal is constructed to be valid for both square and nonsquare systems by using a pseudo-inversion. The existence of the control signal is always assured by employing the method of parameter hopping instead of the conventional projection method.