  This paper introduces two new identification methods for linear quadratic
(LQ) ordinal potential differential games (OPDGs). Potential games are notable
for their benefits, such as the computability and guaranteed existence of Nash
Equilibria. While previous research has analyzed ordinal potential static
games, their applicability to various engineering applications remains limited.
Despite the earlier introduction of OPDGs, a systematic method for identifying
a potential game for a given LQ differential game has not yet been developed.
To address this gap, we propose two identification methods to provide the
quadratic potential cost function for a given LQ differential game. Both
methods are based on linear matrix inequalities (LMIs). The first method aims
to minimize the condition number of the potential cost function's parameters,
offering a faster and more precise technique compared to earlier solutions. In
addition, we present an evaluation of the feasibility of the structural
requirements of the system. The second method, with a less rigid formulation,
can identify LQ OPDGs in cases where the first method fails. These novel
identification methods are verified through simulations, demonstrating their
advantages and potential in designing and analyzing cooperative control
systems.
