Mathematical Science: Nonlinear Control Theory: Topics Related to Stabilizability, Observability and Realizability

9403924王/林 本研究将探讨非线性控制理论中的两个主要领域。第一个是与控制系统的稳定性和可镇定性，第二个是可观测性和可达性。在稳定性领域内，研究计划将依赖于三个密切相关的主题的整合，最终目标是了解干扰对控制设计的影响。 第一个主题着重于通过分析可达集的结构和它们的关系来分析一般动力系统的稳定性，从而可以开发出一般动力系统的匡威李雅普诺夫函数。 第二个主题是关于所谓的输入状态稳定性，第三个主题是关于设计显式稳定反馈律的通用公式的发展。本研究的第二个主要领域的主要目标是分析系统的不同表示之间的关系。 注意力将集中在澄清不同的概念和结果之间的联系有关的可观测性已开发的微分代数和微分几何的框架内。也要调查的条件下，状态空间系统承认积分输入/输出方程。 粗略地说，控制理论关注的是改变动态系统的行为，以满足期望的性能目标。控制系统的分析和设计在制造自动化和许多其他应用中起着基础作用。本研究的主要问题是受干扰控制系统的稳定性问题，即如何保证感兴趣的量最终以适当的方式表现，而不管作用在系统上的干扰的具体性质，以及系统的识别，即如何获得系统的模型，或“工厂”，根据从观察其运行所获得的数据。 ***

9403924 Wang/Lin Two major areas within nonlinear control theory will be pursued in this investigation. The first is related to stability and stabilizability of control systems, and the second to observability and reachability. Within the area of stability, the research program will rely upon the integration of three closely related topics with the ultimate goal of developing an understanding of the effect of disturbances on control design. The first topic focuses on the analysis of the stability of general dynamical systems through an analysis of the structure of reachable sets and their prolongations, so that a converse Lyapunov function for general dynamical systems can be developed. The second topic concerns so-called input-to-state stability, and the third topic concerns the development of universal formulae for designing explicit stabilizing feedback laws. The main goal in the second major area of this investigation is to analyze the relationship between different representations of systems. Attention will be focused on clarifying the connections between different notions and results related to observability which have been developed within the frameworks of differential algebra and differential geometry. Also to be investigated are conditions under which a state space system admits integral input/output equations. Roughly speaking, control theory concerns itself with changing the behavior of dynamical systems so as to meet desired performance objectives. The analysis and design of control systems play fundamental roles in manufacturing automation and many other applications. The main issues addressed in this research deal with the problem of stability of control systems subject to disturbances, that is, with the question of how to assure that the quantities of interest ultimately behave in an appropriate manner regardless of the specific nature of the disturbances acting on the system, and with identification of systems, that is, with the questi on of how to obtain models of the system, or "plant", on the basis of data obtained from observations of its operation. ***