Nonlinear Network Structures for Dynamic System Control

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AbstractThe complexity of modem day aerospace, industrial, DoD, civil infrastructure, and vehicle systems is increasing, and performance requirements are becoming more stringent in terms of both accuracy and speed of response. Such systems are characterized by complex dynamics having nonlinearities, unmodeled dynamics, flexibility effects, varying parameters, unknown friction, high amplitude disturbances, and actuators with deadzones, backlash, and saturation. The control problems associated with such complex systems are not easy, as they do not satisfy most of the assumptions made in the controls literature. Therefore, most existing control algorithms do not work well. Optimal nonlinear control systems hold out the hope of successfully confronting these problems but are expressed in terms of solutions to the Hamilton-Jacobi-Bellman (HJB) equation. However, HJB is not analytically solvable for practical systems, and the dynamic programming solution for discrete-time systems suffers from NP-complexity problems ('the curse of dimensionality'). Approximate solution techniques for the HJB equation have been explored and show great promise in reducing NP-complexity issues. However, such HJB approximate techniques must be tied to real-time on-line feedback control techniques that simultaneously stabilize the system while adapting to approximate the HJB solution.Recent developments show that nonlinear network structures, both neural network (NN) and fuzzy logic (FL) systems, hold out the hope of providing approximate solutions to the HJB equation and other nonlinear design equations. Structured nonlinear networks hold out the hope for confronting problems of NP-complexity in complex systems control. The structure inherent in FL systems holds out the hope of designing new NN architectures of increased structure. Approximate HJB solution also holds out the hope of bridging the gap between high-level computer science architectures and servo-level feedback control. This research has three goals: (1) Nearly Optimal HJB Control Using Neural Networks; (2) 0N0ovel 00002High-Level Nonlinear Network Control Architectures; (3) and UTA/High School Teams and Courseware for Nonlinear Network Control.