Invertibility of hybrid systems

目的：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变化。每一种工作模式都由一个具有内部状态、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系统或交换系统。这些系统的一个尚未被研究的重要结构特性是可逆性，即根据测量输出的知识重建未知输入和未知电流操作模式的能力。可逆性可能代表了系统设计中期望的属性，因为它允许人们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，为了确保系统安全，人们可能希望将系统设计成不可逆转的，以确保入侵者无法访问受保护的系统信息。提出的研究目标是开发一种方法来研究混合系统的这一特性。知识价值：本研究的主要理论成果将为研究混合系统可逆性提供一套新的理论工具。这一新理论将依赖于经典的单模系统可逆性理论和更现代的开关和混合系统理论的技术融合，从而将这两个研究方向推向新的前沿。更广泛的影响：可逆性是系统设计和系统安全分析中的一个重要属性。在建议项目中开发的理论工具将为应用中的系统设计提供新的指导方针。文中详细讨论了多智能体网络系统中的拓扑恢复问题。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。建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。倡议将确保通过出版物、特邀讲座、辅导讲习班和网络材料广泛传播和推广成果。

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.