Nonlinear and Adaptive Control with Unmodeled Dynamics

从航空和汽车发动机到微纳米系统的广泛应用，需要多样化的非线性反馈设计，这仍然是一个重要的研究方向。然而，非线性设计方法的可用性的增加必须伴随着对其相对于未建模动力学的鲁棒性的更充分的理解，这在所有工程应用中无处不在。强非线性与未建模的动力学相互作用可能导致不稳定现象，这是线性鲁棒控制方法无法处理的。为了提高非线性设计的适用性，需要新的非线性鲁棒性分析和补偿方法。本提案的两个主要主题是，首先，分析由标称设计模型中未包含的重要动态引起的非线性反馈系统的行为，其次，静态和动态补偿方法，以提高未建模动态存在下的稳定性和性能。在第一部分中简要概述了当前授权下的成就之后，在第二部分中通过简单的示例介绍了未建模动态的影响和可能的补救措施。在第三部分中描述的研究计划，提出了具有最小和非最小相位未建模动力学的系统的深入分析和表征。然后提出了通过补偿和结构特定的稳健重新设计来改善绩效的有希望的方向。

The wide diversity of applications, from aero and automotive engines to micro and nano systems, requires a diversity of nonlinear feedback designs, which remain an important research direction. However, the increased availability of nonlinear design methods must be accompanied with a fuller understanding of their robustness properties with respect to unmodeled dynamics, ubiquitous in all engineering applications. Strong nonlinearities interacting with unmodeled dynamics may cause instability phenomena that cannot be handled by linear robust control methods. New nonlinear robustness analysis and compensation methods are needed to increase the applicability of nonlinear designs. The two main themes in this proposal are, first, analysis of the behavior of nonlinear feedback systems caused by significant dynamics not included in their nominal design models, and, second, static and dynamic compensation methods to improve stability properties and performance in the presence of unmodeled dynamics. After a brief overview of the accomplishments under the current grant in Part One, the effects of unmodeled dynamics and possible remedies are introduced through simple examples in Part Two. The research plan, described in Part Three, proposes an in-depth analysis and characterization of systems with minimum and nonminimum phase unmodeled dynamics. It then suggests promising directions for performance improvement by compensation and structure specific robust redesigns.