Search

Abstract: We give a representation for the closed convex hull of the set of discounted occupational measures generated by control-state trajectories of a deterministic control system. We also investigate the limit behavior of the latter when the discount factor tends to zero and compare it with the limit behavior of the long run time average occupational measures set. The novelty of our results is in that we allow the control set dependence on the state variables that make the results to be applicable to differential inclusions. [Copyright &y& Elsevier]

We consider a model describing a rational behavior of groups or individuals in many real life situations. The model is formulated in terms of an infinite sequence of repeatedly solved finite-time horizon-optimal control problems. The solutions of these problems form a contest preparation process. We show that this processes converges (as time tends to infinity) to some limit periodic or steady-state regimes, which are independent of the initial conditions. [ABSTRACT FROM AUTHOR]