An Entropy Approach to Invariance and Reachability of Uncertain Control Systems with Limited Information

该补助金将研究具有有限信息和可达性（即，最终到达期望区域的能力）和不变性（即，总是保持在期望区域中的能力）目标。在现代控制系统中，诸如通信系统、数字传感器和微处理器之类的数字组件被普遍用于实现闭环控制。利用闭环控制的示例系统包括交通网络、自主运输、电力网络和辅助生活系统。数字和物理组件之间复杂的相互作用在分析和控制这些系统中引入了重大挑战，这些系统无法通过经典控制理论中可用的方法来解决。例如，由于传感器和控制器之间的通信信道的有限带宽，它们之间的信息交换受到限制。考虑到这种有限的信息交换，某些控制目标是否可实现的基本问题不能用经典控制理论来回答。熵的概念（即，系统初始条件不确定性的度量）作为信息度量已被证明是解决这些类型问题的关键概念。本计画将探讨不确定非线性系统之不变性与可达性之熵新概念。该项目的成果将使许多创新的应用，包括水下航行器，传感器网络和工业控制网络的有效部署的第一步。该项目的主要目标是非确定性控制系统的信息措施的分析，以确定实现不变性和可达性属性所需的最低数据速率。此外，本计画也将分析相互连接的非决定性控制子系统的最小资料传输率，以强化基于子系统资料传输率的不变性。具体来说，该项目将引入子系统不变熵的概念，其中整体互连系统的不变熵的上下界是按组成计算的。与有限信息反馈的分析类似，考虑到数字组件，用于解决某些复杂控制目标的控制器的形式化合成是一个无法用经典技术解决的挑战。一个相对较新的方法，即基于抽象的控制器综合方法，已被证明是一个有前途的候选人，以解决这类问题。这个项目将使用开发的信息措施，以量化的计算复杂性的抽象为基础的综合方法。最后，该项目将研究数值算法，使用基于抽象的技术来计算所研究的熵概念的上限。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

This grant will investigate the control of uncertain nonlinear systems with limited information and with respect to reachability (i.e., the ability to eventually reach a desired region) and invariance (i.e., the ability to always remain in a desired region) objectives. Digital components such as communication systems, digital sensors, and microprocessors are being used ubiquitously in modern control systems to implement closed-loop control. Example systems that utilize closed-loop control include traffic network, autonomous transportation, power networks, and assisted living systems. The intricate interactions between the digital and physical components introduces major challenges in the analysis and control of such systems that cannot be addressed by the methods available in classical control theory. For example, due to the finite bandwidth of communication channels between sensors and controllers, information exchange between them is limited. The fundamental question of whether certain control objectives are realizable by taking into account such limited information exchange cannot be answered by classical control theory. The notion of entropy (i.e., a measure of uncertainty in a system’s initial condition) as an information measure has shown to be a key concept in addressing these types of questions. This project will investigate novel notions of entropiesy for invariance and reachability properties for uncertain nonlinear systems. The results of this project will enable the first step towards the efficient deployment of many innovative applications including underwater vehicles, sensor networks, and industrial control networks.The main goal of this project is the analysis of information measures for nondeterministic control systems to determine the minimal data rates necessary for the realization of invariance and reachability properties. In addition, this project will also analyze minimal data rates for interconnected nondeterministic control subsystems to enforce invariance properties based on data rates of subsystems. Specifically, the project will introduce the notion of subsystem invariance entropy, in which lower and upper bounds for the invariance entropy of the overall interconnected system are computed compositionally. Similar to the analysis of limited information feedback, formal synthesis of controllers for solving certain complex control objectives, taking into account the digital components, is a challenge that cannot be addressed with classical techniques. A relatively recent approach, namely, the abstraction-based controller synthesis method, has proven to be a promising candidate to address this class of problems. This project will use the developed information measures to quantify the computational complexity underling the abstraction-based synthesis approach. Finally, the project will research numerical algorithms using abstraction-based techniques to compute upper bounds of the researched entropy notions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.