## Abstract

We consider infinite horizon optimal control problems with time averaging and time discounting criteria and give estimates for the Cesàro and Abel limits of their optimal values in the case when they depend on the initial conditions. We establish that these limits are bounded from above by the optimal value of a certain infinite dimensional (ID) linear programming (LP) problem and that they are bounded from below by the optimal value of the corresponding dual problem. (These estimates imply, in particular, that the Cesàro and Abel limits exist and are equal to each other if there is no duality gap). In addition, we obtain IDLP-based optimality conditions for the long run average optimal control problem, and we illustrate these conditions by an example.

Original language | English |
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Pages (from-to) | 1591-1610 |

Number of pages | 20 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 27 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2022 |

## Keywords

- Optimal control
- Cesàro and Abel limits
- occupational measures
- linear programming
- duality