Symbolic Methods and Tools for Discrete Event Dynamic Systems

Abstract: The interest in Discrete Event Dynamic Systems (DEDS) has increased during the last years, due to the lack of methods and tools that are capable of handling the complexity of problems and tasks present in industry today. In this thesis we will consider a framework based on relations over finite domains. The framework is used for modeling, analysis, and synthesis of DEDS.Binary Decision Diagrams (BDDs) are used to represent relations, as well as the operations for modeling, analysis and synthesis of DEDS. To utilized the structure of integers and arithmetic operation, Integer Decision Diagrams (IDDs) are developed and implemented. Polynomials over finite fields are another type of representation that is used for the relational framework. Here Gröbner bases, and Integrated Monomial Diagrams (IMDs) are the tools that are used. IDDs and IMDs are both developed, by the author, to represent integer structures and arithmetic operations efficiently.With tools for efficient relational representation, it possible to improve scalability of DEDS computations, as shown in this thesis by the modeling and analysis of the landing gear controller of the Swedish fighter aircraft JAS 39 Gripen. A relational model, represented by a BDD, is automatically generated from a 1200 lines Pascal implementation, which contains 105 binary variables of which 26 are state variables. Function specifications expressed with temporal algebra, are verified using tools for dynamic analysis, which we also use to compute a polynomial representing the set of all reachable states in the model. The landing gear controller serves as a benchmark test of BDDs and IDDs. The IDDs reduced the computation time by 50%.To explore the ability and applicability of using a polynomial relational representation when doing synthesis, we use a tank system containing actuators (pump and valves) and sensors (the tank level and measurable disturbances). We propose a synthesis method that uses actuator priority, weighting of states, and Gröbner bases to compute explicit control laws for the actuators, fulfilling the control objectives even if one of the actuators (the pump) is defective.Modeling aspects are emphasized further, by comparing the polynomial approach which we have used, with Boolean expressions and established DEDS approaches in the community of automatic control like Ramadge-Wonham, Petri nets, and COCOLOG. We discuss how to handle transformation between signals and events for DEDS and how to modularize DEDS to gain complexity advantages. Model description languages are discussed and desirable features are stated, using the experiences achieved from the modeling of the tank system and the landing gear controller.

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