Invertibility of hybrid systems

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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.