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

这个项目将把动态系统的熵的一个深刻而直观的概念扩展到受外部扰动的切换系统的控制。与热力学和信息论中有关熵的概念类似，动力系统的熵是对其状态的不确定性的度量--更具体地说，它是对这种不确定性的增长速度的度量。这一熵概念对于控制工程的重要性部分源于它与镇定和抑制干扰这两个基本控制任务的关系。稳定意味着系统在受到扰动后将恢复到其期望的运行状态。干扰抑制意味着系统持续的外部干扰要么不会出现在系统输出中，要么至少会得到高度衰减。为了实现这两个期望目标中的任何一个，都要求必须使用来自系统测量的信息来抵消不确定性的增长--例如，由于开环不稳定动态、外部干扰或有限控制分辨率。使用熵可以将采样率、传感器和执行器分辨率以及通信带宽等方面的重要实用限制严格纳入系统分析和设计程序。在当前的控制工程实践中，这些真正的工程系统的关键要素往往被视为事后的考虑。预计该项目的成果将对自动驾驶汽车和飞行器、化工过程控制以及电网的安全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。熵表征了动力系统状态的不确定性随时间增加的速度。从控制理论的观点来看，熵对应于关于系统的信息必须被传递到控制器以使系统稳定的最小速率。控制理论熵还通知执行其他控制任务所需的信息速率，例如干扰抑制。在这个项目中，这些概念和联系将扩展到切换系统的环境中，对于切换系统，系统行为的分析以及控制任务比非切换情况要复杂得多。该项目有三个主要的理论目标：1)识别有意义的切换系统类，可以计算其熵(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镇定和干扰抑制；以及3)系统地使用熵作为工具来衡量这些控制方案的效率和性能。切换系统描述了许多与工业相关的过程，而控制理论熵的定义扩展到这些系统允许严格处理传感、驱动和通信方面的现实限制。基于熵的分析为现实动力学和控制体系结构的控制提供了统一的分析和设计框架。

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.