Abstract—Techniques for diagnosing faults in hybrid systems that combine digital (discrete) supervisory controllers with analog (continuous) plants need to be different from those used for discrete or continuous systems. This paper presents a methodology for online tracking and diagnosis of hybrid systems. We demonstrate the effectiveness of the approach with experiments conducted on the fuel-transfer system of fighter aircraft. Index Terms—Fault detection and isolation, hybrid systems, model-based diagnosis (MBD). I.

Abstract. WepresentanimplementationinthetheoremproverPVS of co-inductive stream calculus. Stream calculus can be used to model signal flow graphs, and thus provides a nice mathematical foundation for reasoning about properties of signal flow graphs, which are again used to model a variety of systems such as digital signal processing. We show how proofs by co-induction are used to prove equality of streams, and present a strategy to do this automatically. 1

In this paper, we present a technique for estimating the gain, bandwidth, power and area of analog integrated circuits. A two-step approach is adopted to speed up the estimation process and handle larger analog systems. In the first step, the performance of basic analog components is estimated using a knowledge-based approach. Then, component models are generated with the estimates produced at this phase. In the second phase, we use a symbolic analysis methodology to evaluate the performance at the system level. The system net-list is represented by a signal flow graph (SFG) using the component models generated at the previous phase. The SFG approach allows to handle feedback loops at the system level. 1 Introduction The analog synthesis process consists of two phases: topology selection and circuit sizing [1]. During the topology selection process, a net-list of components selected from a pre-defined library is generated. The generated topology should meet the specification requirem...

Techniques from algebra and graph theory are employed as interconnected systems are studied from an abstract point of view. A theory of signal flow graphs over rings is developed which embodies aspects of the theory of linear equations over rings most relevant to large-scale systems. The classic gain formulas of Mason and Riegle are shown to be valid for systems over a commutative and noncommutative ring respectively. A new sufficient condition for existence and uniqueness is introduced, namely, if the cycle products are contained in the Jacobson radical, then the system of linear equations has a unique solution, and the corresponding signal flow graph admits a unique reduction. The technique of ring localization allows the complete characterization of a family of signal flow graphs whose edge operators are in a certain ring and whose cycle products are in a certain ideal. 3 Contents 1

We present early work on a PVS implementation of a model of simple control as signal flow graphs to enable formal verification of input/output behaviour of the control system. As has been shown by Rutten, Signal flow graphs can be described using Escardo's coinductive stream calculus, which includes a definition of di#erentiation for streams over the real numbers and the use of di#erential equations. The basics of coinductive stream calculus has been implemented in PVS.

Topology and static response of interaction networks in molecular biology