Identification methods for ordinal potential differential games

This paper introduces two new identification methods for linear quadratic (LQ) ordinal poten-
tial differential games (OPDGs). Potential games are notable for their benefits, such as the
computability and guaranteed existence of Nash Equilibria. While previous research has ana-
lyzed ordinal potential static games, their applicability to various engineering applications
remains limited. Despite the earlier introduction of OPDGs, a systematic method for iden-
tifying 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 poten-
tial 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. ... mehrThese novel identification methods are
verified through simulations, demonstrating their advantages and potential in designing and
analyzing cooperative control systems.