Nonlinear Network Structures for Dynamic System Control

摘要现代航空航天、工业、国防部、民用基础设施和车辆系统的复杂性正在增加，对响应的准确性和速度的性能要求也变得更加严格。这类系统的特点是具有非线性、未建模的动态、柔性效应、变化的参数、未知的摩擦、高幅度的扰动以及具有死区、间隙和饱和的执行器。与这种复杂系统相关的控制问题并不容易，因为它们不满足控制文献中所做的大多数假设。因此，现有的大多数控制算法都不能很好地工作。最优非线性控制系统希望能够成功地解决这些问题，但可以用Hamilton-Jacobi-Bellman(HJB)方程的解来表示。然而，对于实际系统，HJB不是解析可解的，离散系统的动态规划解存在NP-复杂性问题(“维度灾难”)。HJB方程的近似解技术已经被探索，并显示出在减少NP复杂性问题方面的巨大希望。然而，这样的HJB近似技术必须与实时在线反馈控制技术相结合，这些技术在适应HJB近似解的同时使系统稳定。最近的发展表明，非线性网络结构，包括神经网络(NN)和模糊逻辑(FL)系统，都有望为HJB方程和其他非线性设计方程提供近似解。结构化非线性网络为解决复杂系统控制中的NP复杂性问题提供了希望。FL系统固有的结构为设计新的递增结构的神经网络体系结构提供了希望。近似的HJB解决方案也为弥合高级计算机科学体系结构和伺服级反馈控制之间的差距带来了希望。本研究有三个目标：(1)基于神经网络的近最优HJB控制；(2)新的00002高级非线性网络控制体系结构；(3)UTA/High School团队和非线性网络控制课程。

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.