A coupling approach to estimating the Lyapunov exponent of stochastic max-plus linear systems

• Published in: European journal of operational research Vol. 210; no. 2; pp. 249 - 257
• Main Authors: Goverde, Rob M.P., Heidergott, Bernd, Merlet, Glenn
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.04.2011; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Chaos theory; Computer Science; Computer simulation; Convergence; Discrete Mathematics; Dynamical systems; Estimating techniques; Exact sciences and technology; Game theory; Linear programming; Linear systems; Lyapunov exponent; Lyapunov exponents; Mathematics; Max-plus algebra; Max-plus algebra Stochastic DES Lyapunov exponent Simulation Railway systems; Operational research; Operational research and scientific management; Operational research. Management science; Operations Research; Probability; Railroads; Railway engineering; Railway networks; Railway systems; Sampling; Simulation; Stochastic DES; Stochastic models; Stochasticity; Studies; Railway systems; Simulation; Max-plus algebra; Stochastic DES; Lyapunov exponent; Uncertain system; Linear system; Probabilistic approach; Max plus algebra; Rail transportation; Sampling; Stochastic system
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2010.09.035

This paper addresses the problem of approximately computing the Lyapunov exponent of stochastic max-plus linear systems. Our approach allows for an efficient simulation of bounds for the Lyapunov exponent. We provide sufficient conditions for the convergence of the bounds. In particular, a perfect sampling scheme for the Lyapunov exponent is established. We illustrate the effectiveness of our bounds with an application to (real-life) railway systems.