On a discounted notion of strict dissipativity

Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions using model predictive control schemes, and strict dissipativity. An important feature of these results is that strict dissipativity provides a checkable condition for the other two properties. These results relate to optimal control problems with undiscounted stage cost. Motivated by applications in economics, we consider optimal control problems with discounted stage cost and define a notion of discounted strict dissipativity. As in the undiscounted case, we show that discounted strict dissipativity provides a checkable condition for various properties of the solutions of the optimal control problem associated with the appropriately defined discounted available storage function.