A Special Dynamic Programming Technique for Multiobjective Discrete Control and for Dynamic Games on Graph-Based Networks

In this paper we extend the dynamic programming technique for the multiobjective version of a special class of problems representing a graph-theoretic structure on a certain network. We assume that the dynamics of the system is controlled by p actors (players) and each of them intend to minimize his own integral-time cost which is described by a certain trajectory. Applying Nash and Pareto optimality principles we study the multiobjective control problems on dynamic networks where the dynamics is described by a directed graph. Polynomial-time algorithms for determining the optimal strategies of the players in the considered multiobjective control problems are proposed exploiting the special structure of the underlying graph.