Adaptive Identification and Control of Dynamical Systems Using Neural Networks

0113239纳伦德拉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个标题：（i）不确定性（ii）非线性（iii）复杂性和（iv）时变。 自适应控制是一门处理系统中不确定性的学科，线性系统的自适应控制目前已经得到很好的理解。 当被控对象的特性是已知的但非线性的时，控制问题就变得相当复杂;当被控对象的特性是未知的和/或随时间变化时，控制问题就变得相当棘手。 当神经网络用于控制非线性对象时，会遇到所有四类问题。在过去的十年中，在理解神经控制中出现的问题方面取得了相当大的进展[1]- [18]。 数学建模、系统识别和跟踪期望输出信号的控制器的合成都已被广泛研究。 不同类别的干扰的影响也进行了研究，开发的方法已被应用到广泛的一类实际问题。 尽管如此，许多重要的问题仍然没有得到解答，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。该提案解决了非线性动态系统自适应控制中的三个基本和密切相关的问题。 第一个关注的问题的稳定性和收敛性的神经网络控制和处理的控制器的结构和用于证明稳定性的工具。 第二个问题涉及的重要问题，一般类的非线性系统产生最优控制输入。 在诸如过程控制和飞行器控制等成熟的领域以及诸如机器人和空间技术等新领域中，此类问题越来越频繁地出现。 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。 在这三种情况下的主要问题进行了说明，数学上的困难进行了详细讨论，并提出了潜在的富有成效的途径进行研究。 PI认为，在神经控制发展的目前状态下，提案的三个部分代表了使用神经网络的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.