Nash Equilibrium Controllability of Linear-Quadratic Differential Graphical Games
Zili Wang, Hao Yang, Bin Jiang · 2024
This article considers for the first time Nash equilibrium controllability problem of linear-quadratic (LQ) differential graphical games, that answers the question whether there exists a local standard quadratic performance index such that the Nash equilibrium can reach the desired states and distributed optimal control inputs. A sufficient controllability criterion determined by system dynamics and the desired linear feedback control matrix is established and is easily checkable. Such a criterion is associated with the existence problem of a continuous algebraic Riccati equations’ constrained solution. The new result is also applicable in standard LQ differential games to check the Nash Equilibrium controllability.