This paper presents a framework for modeling faults in hybrid systems that leads to an efficient approach for monitoring and diagnosis of real-time embedded systems. We describe a fault parameterization based on hybrid automata models and consider both abrupt failures and gradual degradation of system components. Our approach also addresses the computational problem of coping with large amount of sensor data by using a discrete event model of the system so as to focus distributed signal analysis on when and where to look for signatures of interest. The approach has been demonstrated for the on-line diagnosis of a hybrid system, the Xerox DC265 printer. 1

This paper presents an efficient online mode estimation algorithm for a class of sensor-rich, distributed embedded systems, the so-called hybrid systems. A central problem in distributed diagnosis of hybrid systems is efficiently monitoring and tracking mode transitions. Brute-force tracking algorithms incur cost exponential in the numbers of sensors and measurements over time and are impractical for sensor-rich systems. Our algorithm uses a model of system's temporal discrete-event behavior such as a timed Petri net to generate a prior so as to focus distributed signal analysis on when and where to look for mode transition signatures of interest, drastically constraining the search for event combinations. The algorithm has been demonstrated for the online diagnosis of a hybrid system, the Xerox DC265 printer. 1

Many networked embedded sensing and control systems can be modeled as hybrid systems with interacting continuous and discrete dynamics. These systems present significant challenges for moni-toring and diagnosis. Many existing model-based approaches focus on diagnostic reasoning assuming appropriate fault signatures have been generated. However, an important missing piece is the integration of model-based techniques with the acquisition and processing of sensor signals and the modeling of faults to support diagnostic reasoning. This paper addresses key modeling and computational problems at the interface between model-based diagnosis techniques and signature analysis to enable the efficient detection and isolation of incipient and abrupt faults in hybrid systems. A hybrid automata model that parameterizes abrupt and incipient faults is introduced. Based on this model, an approach for diagnoser design is presented. The paper also develops a novel mode estimation algorithm that uses model-based prediction to focus distributed processing signal algorithms. Finally, the paper describes a diagnostic sys-tem architecture that integrates the modeling, prediction, and diagnosis components. The implemented

To engineers, scientists, and mathematicians with double X factor ii ACKNOWLEDGEMENTS This thesis reports on work performed while the author was in under the super-vision of Professor Stéphane Lafortune at the University of Michigan. The financial

Abstract — A formulation and solution methodology for ontime fault diagnosis in discrete event systems is presented. This formulation and solution methodology captures the timeliness aspect of fault diagnosis and is therefore different from all other approaches to fault diagnosis in discrete event systems which are asymptotic in nature. A monitor observes a projection of the events that occur in the system. After each observation it can either raise an alarm and shut down the system or allow the system to continue. If the system is stopped when no fault had occurred, a false alarm penalty is incurred; on the other hand if a fault had occurred, a delayed detection penalty is incurred. Both these penalties are trace dependent. The on-time diagnosis problem is formulated as a minimax optimization problem where the objective is to choose a monitoring rule which minimizes the worst case cost along all traces of the language describing the discrete event system. An optimal diagnosis rule is determined using a dynamic programming algorithm. An example is presented which illustrates our methodology and highlights the difference between our formulation of on-time diagnosis with existing results on asymptotic diagnosis of discrete event systems. I.