Switched Control Systems with Limited Information: An Entropy Approach to Stabilization and Disturbance Attenuation

这个项目将扩展一个深刻的和直观的概念熵的动态系统的控制切换系统受到外部干扰。类似于热力学和信息论中熵的相关概念，动态系统的熵是对其状态的不确定性的度量-更具体地说，它是这种不确定性增加速率的度量。熵的概念对于控制工程的重要性部分来自于它与稳定和干扰抑制的基本控制任务的关系。稳定是指系统在受到扰动后将返回到其期望的操作条件。干扰抑制意味着系统的持续外部干扰不会出现在系统输出中，或者至少会被高度衰减。为了实现这些理想的目标中的任何一个，都需要不确定性的增长--例如由于开环不稳定动态、外部干扰或有限的控制分辨率--必须使用来自系统测量的信息来抵消。熵的使用允许重要的实际限制采样率，传感器和执行器的分辨率，和通信带宽，严格纳入系统的分析和设计程序。这些真实的工程系统中至关重要的元素在当前的控制工程实践中往往被视为事后的想法。该项目的成果预计将对自动驾驶汽车和飞行器、化学过程控制以及电网的安全性和可靠性等应用产生重大影响。该项目还包括将基础研究与人员培训和教育活动相结合的组成部分。熵表征动态系统状态的不确定性随时间增加的速率。从控制理论的角度来看，熵对应于系统信息必须传递给控制器以稳定系统的最小速率。控制理论熵还告知执行其他控制任务（例如干扰衰减）所需的信息速率。在这个项目中，这些概念和连接将在切换系统的背景下进行扩展，对于切换系统，系统行为的分析以及控制它的任务比非切换情况复杂得多。该项目有以下三个主要的理论目标：1）确定有意义的切换系统的类别，（或其合理的紧界）; 2）设计编码和控制策略，以实现基于有限数据速率反馈的切换系统的稳定和干扰衰减; 3）系统地使用熵作为工具来测量这些控制方案的效率和性能。切换系统描述了许多工业相关的过程，控制理论熵的定义扩展到这些系统，允许严格处理传感，驱动和通信的现实限制。基于熵的分析承诺一个统一的分析和设计框架的控制现实的动力学和控制架构。

This project will extend a deep and intuitive notion of the entropy of a dynamic system to the control of switched systems subject to external disturbances. Similarly to related concepts of entropy from thermodynamics and information theory, the entropy of a dynamic system is a measure of uncertainty about its state -- more specifically, it is a measure of the rate of increase in this uncertainty. The importance of this concept of entropy for control engineering arises in part from its relation to the fundamental control tasks of stabilization and disturbance rejection. Stabilization means that the system will return to its desired operating condition after being perturbed. Disturbance rejection means that a persistent external disruption to the system will either not appear in the system output, or will at least be highly attenuated. For either of these desirable objectives to be achieved, it is required that the uncertainty growth -- due, for example, to open-loop unstable dynamics, external disturbances, or finite control resolution -- must be counteracted using information from measurements of the system. The use of entropy allows important practical limitations on sampling rates, sensor and actuator resolution, and communication bandwidth, to be rigorously incorporated into systematic analysis and design procedures. These critically important elements of real engineering systems are too often treated as an afterthought in current control engineering practice. The results of this project are expected to have significant impact on applications such as autonomous cars and aerial vehicles, chemical process control, and the safety and reliability of the electric power grid. The project also includes components for integrating basic research with personnel training and educational activities.Entropy characterizes the rate at which uncertainty about the state of a dynamical system increases with time. From the point of view of control theory, entropy corresponds to the minimal rate at which information about the system has to be communicated to the controller in order to stabilize the system. The control-theoretic entropy also informs the information rate needed to perform other control tasks, such as disturbance attenuation. In this project, these concepts and connections will be extended in the context of switched systems, for which the analysis of system behavior, as well as the task of controlling it, are considerably more complicated than the unswitched case. The project has the following three main theoretical goals: 1) to identify meaningful classes of switched systems for which the entropy (or reasonably tight bounds on it) can be calculated; 2) to design encoding and control strategies that achieve stabilization and disturbance attenuation for switched systems based on limited data rate feedback; and 3) to systematically use entropy as a tool to measure efficiency and performance of these control schemes. Switched systems describe many processes of industrial relevance, and the extension of the definition of control-theoretic entropy to these systems allows rigorous treatment of realistic limitations on sensing, actuation, and communication. Entropy-based analysis promises a unified analysis and design framework for control of realistic dynamics and control architectures.