# Necessary Optimality Conditions For Average Cost Minimization Problems

## TL;DR

This paper establishes necessary optimality conditions for average cost control problems with unknown parameters affecting dynamics, cost, and constraints, accommodating non-compact parameter spaces, thus broadening the theoretical framework for uncertain control systems.

## Contribution

It introduces new necessary optimality conditions for control problems with unknown parameters in a general metric space, extending previous results to non-compact parameter sets.

## Key findings

- Derived necessary conditions for optimality in average cost problems.
- Extended the theory to include non-compact parameter spaces.
- Applicable to control systems with uncertainties in dynamics and constraints.

## Abstract

Control systems involving unknown parameters appear a natural framework for applications in which the model design has to take into account various uncertainties. In these circumstances the performance criterion can be given in terms of an average cost, providing a paradigm which differs from the more traditional minimax or robust optimization criteria. In this paper, we provide necessary optimality conditions for a nonrestrictive class of optimal control problems in which unknown parameters intervene in the dynamics, the cost function and the right end-point constraint. An important feature of our results is that we allow the unknown parameters belonging to a mere complete separable metric space (not necessarily compact).