Max-Plus Algebra and Applications to System Theory and Optimal Control

In the modeling of human activities, in contrast to natural phenomena, quite frequently only the operations max (or min) and + are needed. A typical example is the performance evaluation of synchronized processes such as those encountered in manufacturing (dynamic systems made up of storage and queuing networks). Another typical example is the computation of a path of maximum weight in a graph and more generally of the optimal control of dynamical systems. We give examples of such situations. The max-plus algebra which is a mathematical framework well suited to handle such situations. We present results on i) linear algebra, ii) system theory, iii) duality between probability and optimization based on this algebra.