Identification of stochastic max-plus-linear systems

Abstract

We present a method to identify the parameters of a state space model for a max-plus-linear discrete event system from measured data. Previous papers report on results with noise-free measured data. In this paper we extend this to identification for perturbed max-plus-linear systems in a stochastic setting. The approach is based on recasting the identification problem as an optimization problem. We show that under quite general conditions the resulting optimization problems can be solved very efficiently using gradient search techniques.

Max-plus linear inverse problems: 2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise

“…In the control theory literature this inverse problem is referred to as system identification. For example in [6,14,17,7] the authors present methods for system identification of stochastic max-plus linear control systems. These methods, which can be applied to a very wide class of system, with non-Gaussian noise processes, work by formulating a non-linear programming problem for the unknown system parameters, which is then solved using one of several possible standard gradient based algorithm.…”

Linear regression over the max-plus semiring: algorithms and applications

“…In the control theory literature this inverse problem is referred to as system identification. For example in [5,15,19,6] the authors present methods for system identification of stochastic max-plus linear control systems. These methods, which can be applied to a very wide class of system, with non-Gaussian noise processes, work by formulating a non-linear programming problem for the unknown system parameters, which is then solved using one of several possible standard gradient based algorithm.…”