Dynamical Neural Networks for Modeling and Control of Nonlinear Systems

0115507 Pourboghrat非线性系统的最优控制器设计在过去几年中一直是许多研究的主题。虽然动态线性系统的最优控制器设计已经完全发展，但其非线性扩展仍然是一个研究课题。动态优化的一般框架是变分法和Hamilton-Jacobi-Bellman（HJB）方程。 虽然这些年来的最小化算法已经找到了许多重要的应用，相应的算法通常需要一个两点边值问题的解决方案，这是不适用于在线实现。目前，有几种近似技术可用于最佳调节器设计。这些也可以在线实现，代价是使控制次优。最优跟踪控制器的问题更难，因为近似技术，在一般情况下，不能实现online.This项目将试图开发一个通用的最优控制器的一大类可控和可观的非线性系统。本研究的目的是一个新的通用方法的最优控制器的设计，可以实现在线。所提出的控制架构的关键组成部分是使用一个通用的动态神经网络（DNN）。DNN被证明能够以任意精度逼近任何非线性动态系统，前提是它们具有足够数量的神经元。这个通用模型的非线性系统可以用于推导建议的通用控制器的最优跟踪问题。网络中的权值调整（自适应）问题可以看作是一个等效系统的控制器设计。这使得一个制定两个问题的参数自适应和控制器设计的系统作为一个单一的问题的控制器设计。

0115507PourboghratOptimal controller design for nonlinear systems has been the topic of much research in the past years. Although optimal controller design has been completely developed for dynamic linear systems, its nonlinear extension is still a topic of research. A general framework for dynamic optimization is the calculus of variations and the Hamilton-Jacobi-Bellman (HJB) equation. Although these minimization algorithms over the years have found many important applications, the corresponding algorithm usually requires the solution of a two-point boundary value problem, which is not applicable for on-line implementation. Currently, there are several approximating techniques available that can be used for optimal regulator design. These can also be implemented on-line at the price of rendering the control sub-optimal. The problem of optimal tracking controller is even harder, since the approximating techniques, in general, cannot be implemented on-line.This project will attempt to develop a universal optimal controller for a large class of controllable and observable nonlinear systems. The objective of this research is a new generic approach for the design of optimal controllers that can be implemented on-line. The key component for the proposed control architecture is the use of a generic dynamic neural network (DNN). DNNs are shown to be capable of approximating any nonlinear dynamic system with an arbitrary degree of accuracy, provided that they have enough number of neurons. This generic model of the nonlinear system can be utilized for the derivation of the proposed universal controller for optimal tracking problem. The problem of weight adjustment (adaptation) in the network can be viewed as a controller design for an equivalent system. This allows one to formulate the two problems of parameter adaptation and controller design for a system as single problem of controller design.