Intelligent optimal control with dynamic neural networks.

The application of neural networks technology to dynamic system control has been constrained by the non-dynamic nature of popular network architectures. Many of difficulties are-large network sizes (i.e. curse of dimensionality), long training times, etc. These problems can be overcome with dynamic neural networks (DNN). In this study, intelligent optimal control problem is considered as a nonlinear optimization with dynamic equality constraints, and DNN as a control trajectory priming system. The resulting algorithm operates as an auto-trainer for DNN (a self-learning structure) and generates optimal feed-forward control trajectories in a significantly smaller number of iterations. In this way, optimal control trajectories are encapsulated and generalized by DNN. The time varying optimal feedback gains are also generated along the trajectory as byproducts. Speeding up trajectory calculations opens up avenues for real-time intelligent optimal control with virtual global feedback. We used direct-descent-curvature algorithm with some modifications (we called modified-descend-controller-MDC algorithm) for the optimal control computations. The algorithm has generated numerically very robust solutions with respect to conjugate points. The adjoint theory has been used in the training of DNN which is considered as a quasi-linear dynamic system. The updating of weights (identification of parameters) are based on Broyden-Fletcher-Goldfarb-Shanno BFGS method. Simulation results are given for an intelligent optimal control system controlling a difficult nonlinear second-order system using fully connected three-neuron DNN.