Parameter-Invariant Monitor Design for Cyber-Physical Systems

With recent advances in low-power low-cost communication, sensing, and actuation technologies, Cyber Physical Systems (CPS) have revolutionized automated medical diagnostics and care, building energy management, and smart grids. With this revolution, dawns a new era of CPS monitoring where fusing measurements from multiple devices provides unprecedented early detection of critical events. However, some applications (e.g. medical diagnostics) explicit models and/or rich training data relating available measurements to events are unavailable or impractical. Under these troublesome scenarios, this tutorial presents a parameterinvariant approach to monitor design which has successful in developing monitors for medical conditions, building control failures, and network disturbances. Owing its mathematical origin to the robust radar signal processing literature, the parameter-invariant approach to is presented as consisting of three components: (1) foundations of parameter-invariant design, (2) modeling CPS for parameter-invariance, and (3) applied parameter-invariant monitoring. To illustrate each component, the tutorial makes extensive use of case study monitors related to medical alarms (e.g. hypoxia, hypovolemia, and hypoglycemia), building energy management, and power grids. The foundations of parameter-invariant design consists of a design philosophy aimed at providing a monitor robust to nuisance artifacts/parameters in the data. This ultimately requires the co-design of physical models and test statistics such that maximal invariance is achieved with respect to the nuisances. In this component, we first motivate the robust monitoring problem using real-world monitoring applications, and then present the mathematical foundations for parameter-invariant design, making extensive use of simple illustrative examples. While there are many approaches to CPS modeling, the parameter-invariant design utilizes a lumped-parameter linear time-invariant model of the physical dynamics coupled with a sequential hypothesis testing approach. The lumpedparameter model is constructed to capture the general trends associated with the monitoring event, while the sequential parameter invariant testing eliminates three common transformations namely: translation, scale, and rotation. This component concludes by providing a general hypothesis testing form for which a parameter-invariant test is optimal. The final tutorial component applies the parameter invari-