Adaptive Identification and Control of Dynamical Systems Using Neural Networks

在设计动态系统控制器时遇到的数学困难可以大致分为四类：(I)不确定性；(Ii)非线性；(Iii)复杂性；(Iv)时变性。自适应控制是一门研究系统不确定性的学科，目前对线性系统的自适应控制已有了很好的认识。当对象特性已知但非线性时，控制问题变得更加复杂；当对象特性未知和/或随时间变化时，控制问题变得真正令人敬畏。当神经网络用于控制非线性对象时，所有这四类问题都会遇到。在过去的十年里，在理解神经控制中出现的问题方面取得了长足的进步[1]-[18]。数学建模、系统辨识和控制器综合以跟踪期望的输出信号都得到了广泛的研究。还研究了不同类型扰动的影响，所发展的方法已应用于广泛的实际问题。尽管如此，许多重要的问题仍然没有得到回答，神经控制器的设计在许多情况下仍然是一门艺术而不是一门科学。该建议解决了非线性动态系统自适应控制中三个基本且密切相关的问题。第一个问题涉及基于神经网络的控制的稳定性和收敛问题，涉及控制器的结构和用于证明稳定性的工具。第二个问题涉及为一般类型的非线性系统生成最优控制输入的重要问题。无论是在过程控制和飞机控制等成熟领域，还是在机器人和空间技术等新领域，此类问题都在日益频繁地出现。最后，第三个问题涉及在快速变化的环境中使用多个模型来有效地控制非线性系统。在所有三种情况下，主要问题都被陈述，数学困难被详细讨论，并提出了潜在的富有成效的研究途径。PI认为，在目前神经控制的发展状况下，该提案的三个部分代表了利用神经网络进行非线性自适应控制的三个密切相关和重要的方面。

0113239NarendraThe mathematical difficulties encountered in designing controllers for dynamical systems can be broadly classified under four headings: (i) uncertainty (ii) nonlinearity (iii) complexity, and (iv) time-variations. Adaptive control is the discipline which deals with uncertainty in systems, and the adaptive control of linear systems is currently well understood. The problem of control becomes substantially more complex when the plant characteristics are known but nonlinear, and becomes truly formidable when they are unknown and/or vary with time. All four classes of problems are encountered when neural networks are used to control nonlinear plants.During the past ten years considerable progress has been made in understanding the problems that arise in neurocontrol [1]- [18]. Mathematical modeling, system identification, and synthesis of controllers to track desired output signals have all been extensively studied. The effect of different classes of disturbances have also been investigated, and the methods developed have been applied to a wide class of practical problems. In spite of this, many important questions remain unanswered, and the design of neural controllers remains in many cases more an art than a science.The proposal addresses three fundamental and closely related questions in the adaptive control of nonlinear dynamical systems. The first concerns questions of stability and convergence of neural network based control and deals with both the structure of the controllers and the tools used for proving stability. The second question deals with the important problem of generating optimal control inputs for general classes of nonlinear systems. Such problems are arising with increasing frequency in both well established areas such as process control and aircraft control, as well as new areas such as robotics and space technology. Finally, the third problem deals with the use of multiple models for controlling efficiently nonlinear systems in rapidly varying environments. In all three cases the principal questions are stated, the mathematical difficulties are discussed in detail, and potentially fruitful avenues for research are proposed. It is the opinion of the PI that, in the present state of development of neurocontrol, the three parts of the proposal represent three closely related and important aspects of nonlinear adaptive control using neural networks.