Indirect adaptive neuro - fuzzy control based on High Order Neural Network Function approximators

The regulation of unknown nonlinear dynamical systems using an indirect adaptive control technique is considered in this paper. The proposed scheme uses the concept of Fuzzy Dynamical Systems (FDS) operating in conjunction with High Order Neural Network Functions (F-HONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of a fuzzy dynamical system (FDS) and in the sequel the fuzzy rules are approximated by appropriate HONNFs. Thus the identification scheme leads up to a Recurrent High Order Neural Network, which however takes into account the fuzzy output partitions of the initial FDS. Once the system is identified around an operation point is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The applicability of the method is tested on a DC Motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation.