This paper presents fuzzy wavelet neural network (FWNN) models for prediction and identification of nonlinear dynamical systems. The proposed FWNN models are obtained from the traditional Takagi-Sugeno-Kang fuzzy system by replacing the THEN part of fuzzy rules with wavelet basis functions that have the ability to localize both in time and frequency domains. The first and last model use summation and multiplication of dilated and translated versions of single-dimensional wavelet basis functions, respectively, and in the second model, THEN parts of the rules consist of radial function of wavelets. Gaussian type of activation functions are used in IF part of the fuzzy rules. A fast gradient-based training algorithm, i.e., the Broyden-Fletcher-Goldfarb-Shanno method, is used to find the optimal values for unknown parameters of the FWNN models. Simulation examples are also given to compare the effectiveness of the models with the other known methods in the literature. According to simulation results, we see that the proposed FWNN models have impressive generalization ability.

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Fuzzy logic systems have been recognized as a robust and attractive alternative to some classical control methods. The application of classical fuzzy logic (FL) technology to dynamic system control has been constrained by the nondynamic nature of popular FL architectures. Many difficulties include large rule bases (i.e., curse of dimensionality), long training times, etc. These problems can be overcome with a dynamic fuzzy network (DFN), a network with unconstrained connectivity and dynamic fuzzy processing units called "feurons." In this study, DFN as an optimal control trajectory priming system is considered as a nonlinear optimization with dynamic equality constraints. The overall algorithm operates as an autotrainer for DFN (a self-learning structure) and generates optimal feed-forward control trajectories in a significantly smaller number of iterations. For this, DFN encapsulates and generalizes the optimal control trajectories. By the algorithm, the time-varying optimal feedback gains are also generated along the trajectory as byproducts. This structure assists the speeding up of trajectory calculations for intelligent nonlinear optimal control. For this purpose, the direct-descent-curvature algorithm is used with some modifications [called modified-descend-controller (MDC) algorithm] for the nonlinear optimal control computations. The algorithm has numerically generated robust solutions with respect to conjugate points. The minimization of an integral quadratic cost functional subject to dynamic equality constraints (which is DFN) is considered for trajectory obtained by MDC tracking applications. The adjoint theory (whose computational complexity is significantly less than direct method) has been used in the training of DFN, which is as a quasilinear dynamic system. The updating of weights (identification of DFN parameters) are based on Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Simulation results are given for controlling a difficult nonlinear second-order system using fully connected three-feuron DFN.