Switched Control Systems

本研究的总体目标是开发综合和分析基于逻辑的开关控制系统的方法。基于逻辑的切换控制器是指这样的控制器，其子系统不仅包括熟悉的动态组件{积分器、加法器、增益等}，但也包括逻辑驱动的元件。这类系统的一个重要类别是那些由一个连续时间的过程控制，一个家庭的固定增益或可变增益的候选控制器，和一个“事件驱动的切换逻辑”称为监督，其工作是确定在真实的时间控制器应适用于该过程。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。首先，我们建议改进和扩展的概念，监督控制介绍了我们以前的工作，第二，使用监督控制作为一个激励车辆的基本问题的研究，在新出现的领域的混合动力systems.The监督控制系统，我们建议研究属于自适应控制系统的范畴。自适应控制已经研究了很多年。然而，尽管已经取得了许多进展，有重大的悬而未决的问题，抑制概念转化为实践：为什么，例如，它仍然是如此难以解释的非专家为什么一个特定的算法是能够正确的功能，在面对未建模的过程动态和L有界噪声？一个给定的算法在失去环路稳定性之前能容忍多少未建模的动态？我们如何选择自适应控制算法的许多设计参数，以实现良好的干扰抑制，瞬态响应等？这项研究的一个主要目标是回答这些问题，并在这样做，使适应性控制更容易获得的从业者。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力学范数界，干扰到受控输出增益等等。我们的最终目标是揭示开发真正的计算机所需的想法-辅助自适应控制的设计方法，它更多地依赖于设计原则，而不是试验和错误的技术。为此，我们将寻求新的切换算法的监督这些控制系统比现有的控制系统更易于分析。我们将继续我们的研究切换动力系统的稳定性，我们将试图得出这样的系统的输入输出特性的构成动力系统的输入输出特性被切换方面的结论。我们将探讨切换动力系统的稳定性和相关的李代数被切换的组成动力系统的向量场所产生的属性之间的联系。我们将研究“覆盖”候选控制器的连续体的问题，所述候选控制器被设计成使得至少一个能够调节过程P，所述过程P的不确定模型位于候选过程模型M的相关联的连续体中，选择候选控制器C的有限集合，使得对于M中的每个模型，C中至少有一个满意的控制器。利用前面的，我们将寻求开发一个可证明正确的approoach监督控制不确定的非线性过程，利用尽可能的范围内，建立非自适应控制设计技术，并考虑到未建模的动态和外源噪声。

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.