On a discounted notion of strict dissipativity*

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Abstract:

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.

Keywords

Nonlinear Systems
Dissipativity
Optimal Control

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*

C.M. Kellett and L. Grüne are supported by Australian Research Council Discovery Project DP160102138. L. Grüne is supported by the Deutsche Forschungsgemeinschaft, Grant GR 1569/13-1. The paper was written while L. Grüne was visiting the University of Newcastle.

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