University of Birmingham > Talks@bham > Optimisation and Numerical Analysis Seminars > Stability of max-plus algebraic discrete event systems

Stability of max-plus algebraic discrete event systems

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If you have a question about this talk, please contact Sergey Sergeev.

The modelling, analysis, and control of the system evolution defined over events results in the discrete-event systems framework. Examples include manufacturing and transportation networks. Max-plus algebra, with maximisation and addition as its basic operations,(and associated algebraic structures) conveniently handle the timing aspects of discrete-event systems when the schedule of operation of different tasks, such as order of trains, is made deterministic. We model discrete-event systems using a hybrid dynamical systems approach where purely (max-plus) algebraic models, derived from timing constraints among events, are en- riched with automata-theoretic conflict resolution schemes to treat variable schedules. In this talk, I will present a Lyapunov-theoretic framework for studying stability of hybrid models in max-plus algebra. Then I present the application of the proposed framework to study boundedness of trajectories generated by a semigroup of matrices in the max-plus algebra. The resulting decision problems are then formulated as mixed-integer programs. I close the presentation with a brief discussion on the complexity of the decision problems.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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