On the persistent excitation conditions of adaptive fuzzy systems in nonlinear identifications

This paper addresses the persistent excitation conditions of adaptive fuzzy systems in the identifications of nonlinear functions and nonlinear dynamical systems. The adaptive fuzzy system is constructed as a standard fuzzy system and the parameters in the fuzzy system are tuned on-line by the orthogonal projection algorithm. We first give the conditions under which the parameters in the fuzzy system can be uniquely determined, and then propose methods to design input signals with the persistent excitation property for adaptive fuzzy systems in the identifications of nonlinear moving average and auto-regressive moving average systems