Trajectory priming with dynamic fuzzy networks in nonlinear optimal control

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.