Algebraic Methods for Verification and Control of Discrete Event Dynamic Systems

Abstract: Discrete event dynamic systems (DEDS) have become increasingly important in industry and there is a need for structured methods applicable to the design process of DEDS. In this thesis we consider algebraic methods for verification and control of DEDS.To model DEDS we use polynomials in a quotient ring. The polynomials are a compact way of representing DEDS and they can also be used for computations. We show that the polynomials can be used to modeland analyze industrial size systems, by applying the algebraic methods to the landing gear controller of the Swedish fighter aircraft JAS 39 Gripen. The polynomial model is generated semi-automatically from the existing Pascal implementation of the controller code and it contains 105 binaryvariables of which 26 are state variables. The set of reachable states is computed and utilized to reduce the size of the model. The reduced model is then used to verify selected function specifications expressed in terms of temporal algebra.We also address the problem of control synthesis for DEDS. Using an example system (a water tank) we study the process of controller design, using polynomials and repeated Gröbner basis computations. The control criteria can include both forbidden states and a desired behavior for the system. Additional requirements are added to generate a unique control law, which is easily translated into implementable code.The results from the tank example are generalized and we show that we can solve a simultaneous supervision and control problem for an untimed DEDS. We discuss the Gröbner basis method and briefly outline an alternative computational method, which probably is better from a complexity point of view but does not produce a unique control law. Finally we compare the proposed polynomial approach with three other approaches within the field.

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