Global optimal control of perturbed systems

We propose a new numerical method for the computation of the optimal value function of perturbed control systems and associated globally stabilizing optimal feedback controllers. The method is based on a set oriented discretization of state space in combination with a new algorithm for the computation of shortest paths in weighted directed hypergraphs. Using the concept of a multivalued game, we prove convergence of the scheme as the discretization parameter goes to zero

Economic receding horizon control without terminal constraints

International audienceWe consider a receding horizon control scheme without terminal constraints in which the stage cost is de ned by economic criteria, i.e., not necessarily linked to a stabilization or tracking problem. We analyze the performance of the resulting receding horizon controller with a particular focus on the case of optimal steady states for the corresponding averaged in nite horizon problem. Using a turnpike property and suitable controllability properties we prove near optimal performance of the controller and convergence of the closed loop solution to a neighborhood of the optimal steady state. Several examples illustrate our ndings numerically and show how to verify the imposed assumptions