Boundedly optimal control of piecewise deterministic systems

This paper deals with a class of undiscounted pieceise deterministic control problems with bounded state space and possibly undiscounted cost. The concept of boundedly optimal control is introduced for undiscounted cost problems. This optimality concept is stronger than the average cost optimality. Via a linit argument for a family of associated problems with discounted cost, the authors show that a dynamic programming formalism can be developed for the characterization of boundedly optimal solutions.