New Trends in Neuro-Fuzzy Adaptive Control Systems
Manolis A. Christodoulou, Yiannis S. Boutalis · 2008
We use a new definition of Neuro-Fuzzy Dynamical Systems, using the concept of Fuzzy Dynamical Systems (FDS) in conjunction with High Order Neural Network Functions (F- HONNFs). The dynamical System is assumed nonlinear and totally 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 HONNF's. Thus the identification scheme leads to a Recurrent High Order Neural Network, which however, takes into account the fuzzy output partitions of the initial FDS. The proposed scheme does not require a priori experts' information on the number and type of input variable membership functions, making it less vulnerable to initial design assumptions. After the identification process we adaptively control the system indirectly. By doing so, we present weight updating laws for the involved HONNs. With rigorous proofs we guarantee that the errors converge to zero exponentially fast, or at least become uniformly ultimately bounded. At the same time we guarantee stability by proving that all signals in the closed loop remain bounded. During both the identification and control process we assume, first that we know the centers and shapes of membership func- tions, and we identify the HONN parameters in which case we get a directional variation. Thus in order to guarantee existence of the control law, we define a new method replacing the well known projection, which is termed parameter hopping and thus we rigorously prove existence of the control law, guaranteeing stability properties. Simulations illustrate the potency of the method and com- parisons with conventional approaches are given. The simulation tests are based on benchmark examples. Also, 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.