Print Email Facebook Twitter Approximation Methods in Stochastic Max-Plus Systems Title Approximation Methods in Stochastic Max-Plus Systems Author Safaei Farahani, S. Contributor De Schutter, B. (promotor) Faculty Mechanical, Maritime and Materials Engineering Department Delft Center for Systems and Control Date 2012-11-28 Abstract Stochastic max-plus systems belong to a special class of discrete-event systems. This class consists of systems with synchronization but no choice and the models of such systems are defined using the operators maximization and addition. Stochastic max-plus systems can be further extended to stochastic switching max-plus systems and stochastic min-max-plus-scaling systems. In the identification and control problem of all these systems, the objective function appearing in the optimization problem can be written as the expected value of the maximum of several affine expressions. The focus of this thesis is on finding an efficient method to compute this expected value since the currently available methods are both too complex and too time-consuming. To address this issue, this thesis proposes an approximation method based on the higher-order moments of a random variable. By considering the relationship between the infinity-norm and the p-norm of vectors, we obtain an upper bound for the expected value of the maximum of several affine expressions. This approximation method can be applied to any distribution that has finite moments and in the case that these moments have a closed form (such as for a uniform distribution, normal distribution, beta distribution, or gamma distribution), the approximation method results in an analytic expression. For all the above-mentioned systems, we have compared the performance of the proposed approximation method with other available methods, such as analytic and numerical integration, and Monte Carlo simulation. In nearly all cases, the computation time of the proposed approximation method is at least two orders of magnitude smaller than that of other methods, while still resulting in a comparable control performance. Subject stochastic max-plus linear systemsmodel predictive controlapproximation methodsmoments of random variablesswitching max-plus linear systemsmax-min-plus-scaling systems To reference this document use: https://doi.org/10.4233/uuid:5cccc163-0b08-4922-9c63-3c469c98530d ISBN 9789462032194 Part of collection Institutional Repository Document type doctoral thesis Rights (c) 2012 Safaei Farahani, S. Files PDF Proefschirft_Samira.pdf 1.06 MB Close viewer /islandora/object/uuid:5cccc163-0b08-4922-9c63-3c469c98530d/datastream/OBJ/view