Data-driven cost representation for optimal control and its relevance to a class of asymmetric linear quadratic dynamic games

Motivated by the fact that optimal performance criteria are often not known a priori, we present an approach to represent quadratic objective functions in the context of optimal control directly using finite, open-loop, non-optimal data trajectories of the state, input and a performance variable. Combined with a data-based representation of linear time-invariant systems this allows us to solve linear quadratic regulator problems with unknown dynamics and unknown cost matrices via data-dependent convex programmes. We show that this result is relevant to a specific class of linear quadratic games, in which one player is missing information regarding the control objectives of the other players and/or the system dynamics. The applicability of the presented results is highlighted via an example concerning human-robot interaction.