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The basic motivation for the research presented in this article is the fact that things go wrong. With the growing complexity of todays engineering systems, the need has arisen for systematic approaches to failure diagnosis. This paper presents an approach for modeling and diagnosis of systems that fall in the area of discrete event dynamic systems. We use a relational framework for discrete event dynamic systems focusing on a conceptually simple representation of the relationships between inputs, outputs and states of a discrete event system. A fault is said to be detectable if there exists a transition in the system model that leads to a detection in a finite number of steps. The transition necessary for detection can automatically be computed from the system model under certain conditions. We also show how to compute the finest possible fault partition under a single fault assumption.

Symbolic algebraic analysis techniques are applied to the landing gear subsystem in the Swedish fighter aircraft, JAS 39 Gripen. Our methods are based on polynomials over finite fields (with Boolean algebra and propositional logic as special cases). Polynomials are used to represent the basic dynamic equations for the processes (controller and plant) as well as static properties of these. Temporal algebra (or temporal logic) is used to represent specifications of system behaviour. These specifications are verified both on a model of the landing gear controller, and a model of the closed loop behaviour of the landing gear controller connected to a plant. The model of the landing gear controller is made from the actual implementation in Pascal. The tools used are developed by the authors in Mathematica and uses an efficient implementation of binary decision diagrams.

Symbolic algebraic modeling and analysis techniques for DEDS are applied to the landing gear subsystem in the new Swedish fighter aircraft, SAS 39 Gripen. The authors' methods are based on polynomials over finite fields. Polynomials are used to represent the basic dynamic equations for the processes (controller and plant) as well as static properties of these. Temporal algebra (or temporal logic) is used to represent specifications of system behavior. The authors use this approach to model the landing gear controller from the complete implementation in Pascal. The authors also provide temporal algebra interpretations of the specifications made available to them. Finally the authors perform a number of symbolic analyses on the complete process (controller and plant). This project is a first demonstration of possible uses of these methods and tools and it shows that these methods and tools scale to a problem of a non-trivial size, i.e. of the size found in complex system designs such as the JAS 39.

This document formulates and solves a number of problems associated with reachability for polynomial dynamical systems over finite fields. This class of systems is intended as a general model class for Discrete Event Systems.