An approximation approach for identification of stochastic max-plus linear systems

Reference:
S.S. Farahani, T. van den Boom, and B. De Schutter, "An approximation approach for identification of stochastic max-plus linear systems," Proceedings of the 18th IFAC World Congress, Milan, Italy, pp. 8241-8246, Aug.-Sept. 2011.

Abstract:
Max-plus linear systems belong to a special class of discrete-event systems that consists of systems with synchronization but no choice. Our focus in this paper is on stochastic max-plus linear systems, i.e., perturbed systems that are linear in the max-plus algebra. One interesting topic is the identification of such systems. Previous works report on a method for identifying the parameters of a state space model for a stochastic max-plus linear system from measured data. However, due to the structure of such systems, this method results in a complex identification problem. Therefore, the aim of this paper is to decrease the computational complexity and the computation time of this problem. To this end, we use an approximation approach that is based on the higher-order raw moments of a random variable. This method results in a less complex problem that can be solved efficiently using gradient search techniques.