On the optimal control of linear systems depending upon a parameter and with missing data

Abstract

The aim of this paper is to study general and abstract control systems with incomplete data. Actually, we introduce the notions of averaged no-regret control and its approximation, the averaged low-regret control to get a full characterization for the optimal control via an optimality system. As an example, we apply the described theory on an optimal control problem for an equation of vibrating thin plate depending on an uncertainty parameter and with missing initial conditions where optimality systems characterizing the averaged no-regret control and the averaged low-regret control are given.