Invertibility of hybrid systems

目的：该研究研究可以在几种不同模式下运行的系统，其中一些离散动力学控制模式的变化。每种操作模式都由具有内部状态、外部输入（可以认为是干扰或控制信号）和测量输出的动态系统来描述。这样的系统被称为混合或切换系统。这些系统的一个重要的结构特性尚未被研究的是可逆性，这是一个未知的输入和未知的电流模式的操作从测量输出的知识重建的能力。可逆性可以代表系统设计中所需的属性，因为它允许从观察到的数据推断系统配置（以操作模式为特征）和外部影响（以输入为特征）。或者，为了确保系统的安全性，人们可能希望将系统设计为不可逆的，以确保入侵者将不能访问受保护的系统信息。建议的研究的目标是开发一种方法，用于调查此属性的混合动力systems.Intellectual优点：建议的研究的主要理论成果将是一套新的理论工具，用于研究混合动力系统的可逆属性。这种新的理论将依赖于融合技术从经典理论的可逆性的单模系统和从更现代的理论切换和混合系统，从而推动这两个研究方向的新fronters.Broader影响：可逆性是一个重要的属性在系统设计和系统安全分析。在拟议的项目中开发的理论工具将提供新的指导方针，系统设计的应用。在建议中详细讨论的一个特定的应用是多代理网络系统中的拓扑恢复。我们设想在各种其他领域的应用，包括车辆系统，生物系统和电力网络。拟议的研究将通过课程开发和研究生指导自然地与教育相结合。主要研究者将通过出版物、特邀讲座、辅导讲习班和网络材料，确保广泛的成果传播和推广。

Objective:The proposed research studies systems that can operate in several different modes, with some discrete dynamics governing the mode changes. Each mode of operation is described by a dynamical system having an internal state, an external input (which can be thought of as a disturbance or a control signal), and a measured output. Such systems are known as hybrid or switched systems. An important structural property of these systems that has not been investigated is invertibility, which is the ability to reconstruct an unknown input and an unknown current mode of operation from the knowledge of the measured output. Invertibility may represent a desired property in system design, because it allows one to infer the system configuration (characterized by the operating mode) and the external influences (characterized byinputs) from the observed data. Or, to ensure system security, one may want to design the system not to be invertible, in order to ensure that the intruder will not be able to gain access to protected system information. The goal of the proposed research is to develop a methodology for investigating this property for hybrid systems.Intellectual Merit:The main theoretical outcome of the proposed research will be a new set of theoretical tools for studying the invertibility property for hybrid systems. This new theory will rely on a fusion of techniques from the classical theory of invertibility for single-mode systems and from the more modern theory of switched and hybrid systems, thereby pushing both of these research directions to new frontiers.Broader Impacts:Invertibility is an important property in system design and system security analysis. The theoretical tools developed in the proposed project will provide new guidelines for system design in applications. A particular application discussed in detail in the proposal is topology recovery in multi-agent networked systems. We envision applications in a variety of other areas, including vehicle systems, biological systems, and power networks. The proposed research will be naturally integrated with education through course development and graduate student mentoring. The PI will ensure wide result dissemination and outreach through publications, invited lectures, tutorial workshops, and web-based materials.