EIA: Control System Synthesis: Nonlinear Feedback

本文主要研究反馈控制的鲁棒性问题。它有两个主要目标：为某些鲁棒反馈系统设计问题开发有效的数值程序，并探索非线性反馈在鲁棒控制中的优点。关于第一个目标，初步的工作表明，某些控制系统设计问题可以简化为更简单的优化问题，涉及只有有限数量的参数的非线性规划。这将是对目前可用技术的巨大改进。我们将研究这种可能性以及重要的数值细节。第二个目标旨在了解非线性反馈实质上优于线性反馈的控制系统设计问题的类型。在这种情况下，最近已经证明，对于一些设计问题，其中的植物模型具有未知参数，非线性控制提供了巨大的优势。然而，对于植物模型具有大量未建模动力学的情况，非线性反馈并不比线性反馈好。这些结果表明，对于许多控制系统设计问题，已知的对象模型的精度决定了最适合控制该对象的反馈类型。我们将对这一原理进行研究，以确定其在具体控制设计问题中的有效性。

This proposal is concerned with the issue of robustness in feedback control. It has two primary goals: To develop efficient numerical procedures for certain robust feedback system design problems, and to explore the merits of nonlinear feedback in robust control. Regarding the first goal, preliminary work indicates that certain control system design problems can be reduced to simpler optimization problems involving nonlinear programming with only a finite number of parameters. This would represent a dramatic improvement over currently available techniques. This possibility and also the important numerical details will be investigated. The second goal is aimed at understanding the types of control system design problems for which nonlinear feedback is substantially superior to linear feedback. In this context it has recently been demonstrated that for some design problems in which the plant model has unknown parameters, nonlinear control offers enormous advantage. However, for situations where the plant model has substantial unmodeled dynamics, nonlinear feedback is no better than linear feedback. These results indicate that for many control systems design problems, the precision to which the plant model is known determines the type of feedback best suited to control that plant. This principle will be investigated to determine its validity in specific control design problems.