A Novel ARX-Local Model Network for Modeling and Controlling Dynamic Systems

In this paper, the idea of fertilizing fuzzy neural networks with wavelets is borrowed and enhanced to introduce a novel neural network named Auto Regressive eXogenous Local Model (ARXLM) network. The enhanced network has a set of notable features compared with previous published fertilized networks. These features can be summarized as follows. First, the proposed network has a simple and plastic structure. The former is resulted from replacing wavelet neural networks used to fertilize a fuzzy neural network by single wavelet nodes, while the latter is inherited from employing the adaptive resonance theory. Second, the network has a parametric structure that facilitates studying the stability of the proposed network using conventional stability methods. The proposed ARX-LM network basically adopt the philosophy of forming a process be modeled with a set of fuzzy-wavelet submodels. Each submodel comprises a Takagi-Sugeno-Kang (TSK) fuzzy rule fertilized by a wavelet function that determines the contribution of the TSK fired rule. The outputs of these submodels are weighted and summed to produce the final output. The parameters of the proposed network are adapted using the Recursive Least Square (RLS) algorithm and its stability can be proved mathematically using Lyapunove’s direct method. The soundness of the proposed ARXLM network is tested in modeling and controlling non-linear dynamical systems. The proposed ARX-LM network is also employed to develop a long range predictive control scheme for time varying medical systems.