Switched Control Systems

本研究的总体目标是开发基于逻辑的开关控制系统的综合和分析方法。基于逻辑的切换控制器是指其子系统不仅包括熟悉的动态组件（积分器、夏季、增益等），还包括逻辑驱动的元素。此类系统的一个重要类别是由待控制的连续时间过程、一组固定增益或可变增益的候选控制器和一个称为“事件驱动切换逻辑”的监督器组成的系统，其工作是实时确定应将哪个控制器应用于该过程。监控系统的例子包括可重构系统、故障校正系统和某些类型的参数自适应系统。我们建议首先完善和扩展我们早期工作中引入的监督控制的概念，其次将监督控制作为一种激励工具，用于研究新兴的混合动力系统领域的基本问题。我们所研究的监控系统属于自适应控制系统的范畴。自适应控制已被研究多年。然而，尽管已经取得了许多进步，仍有一些未解决的主要问题阻碍了概念向实践的转移：例如，为什么向非专业人士解释为什么特定算法能够在面对未建模的过程动力学和L界噪声时正确运行？在失去环稳定性之前，给定算法可以容忍多少未建模的动态？我们如何选择自适应控制算法的众多设计参数来实现良好的抗扰性、瞬态响应等？这项研究的一个主要目标是回答这些问题，从而使自适应控制更容易为实践者所接受。我们将研究技术，使我们能够更清楚，更简洁地量化未建模的动态范数边界，扰动控制输出增益等。我们的最终目标是揭示开发真正的计算机辅助自适应控制设计方法所需的想法，这种方法更多地依赖于设计原则，而不是试验和错误技术。为此，我们将寻求为监督控制系统推导新的切换算法，这些算法比目前存在的算法更易于分析。我们将继续研究切换动力系统的稳定性，并且我们将尝试根据被切换的本构动力系统的输入输出特性得出关于此类系统的输入输出特性的结论。我们将探讨切换动力系统的稳定性与由被切换的本构动力系统的向量场所产生的相关李代数的性质之间的联系。我们将研究“覆盖”候选控制器连续体的问题，该问题设计为至少有一个能够调节过程P，其不确定模型位于候选过程模型M的相关连续体中，并选择有限的候选控制器C集，以便对于M中的每个模型，在C中至少有一个满意的控制器。我们将寻求开发一种可证明正确的方法来对不确定的非线性过程进行监督控制，该过程尽可能地利用已建立的非自适应控制设计技术，并考虑到未建模的动力学和外源噪声。

The overall objective of this research is to develop methods for synthesizing and analyzing logic-based switching control systems. By a logic-based switching controller is meant a controller whose subsystems include not only familiar dynamical components {integrators, summers, gains, etc.} but logic-driven elements as well. An important category of such systems are those consisting of a continuous-time process to be controlled, a family of fixed-gain or variable-gain candidate controllers, and an "event-driven switching logic" called a supervisor whose job is to determine in real time which controller should be applied to the process. Examples of supervisory control systems include reconfigurable systems, fault correction systems, and certain types of parameter-adaptive systems. We propose first to refine and extend the concept of supervisory control introduced in our earlier work and second to use supervisory control as a motivating vehicle for the study of basic issues in the newly emerging field of hybrid dynamical systems.The supervisory control systems we propose to study fall in the category of adaptive control systems. Adaptive control has been under study for many years. Yet despite the numerous advances which have been made, there are major unresolved issues inhibiting the transfer of concepts into practice: Why, for example, is it still so difficult to explain to a non-expert why a particular algorithm is able to functions correctly in the face of unmodelled process dynamics and L bounded noise? How much unmodelled dynamics can a given algorithm tolerate before loop-stability is lost? How do we choose an adaptive control algorithm's many design parameters to achieve good disturbance rejection, transient response, etc.? A major goal of this research is to answer these questions-and in so doing to make adaptive control much more accessible to practitioners. We will investigate techniques enabling us to much more clearly and concisely quantify unmodelled dynamics norm bounds, disturbance-to-controlled output gains and so on. Our ultimate objective is to lay bare the ideas needed to develop a bona fide computer-aided adaptive control design methodology which relies much more on design principals then on trial and error techniques.Towards this end we will seek to derive new switching algorithms for supervisory control systems which are more amenable to analysis than those which currently exist. We will continue our study of the stability of switched dynamical systems, and we will attempt to draw conclusions about the input-output properties of such systems in terms of the input output properties of the constituant dynamical systems being switched. We will explore the connection between the stability of switched dynamical systems and the properties of the associated Lie algebras generated by the vector fields of the constituient dynamical systems being switched. We will study the problem of `covering' a continuum of candidate controllers designed so that at least one is able to regulate a process P whose uncertain model lies in an associated continuum of candidate process models M, with a finite set of candidate controllers C chosen so that for each model in M there is at least one satisfactory controller in C. Using the preceding, we will seek to develop a provably correct apporoach to supervisory control for uncertain nonlinear processes which exploits to the extent possible, established non-adaptive control design techniques and which takes into account both unmodelled dynamics and exogeneous noise.