Differential Graphical Games

This chapter deals with the formulation and online approximate feedback-Nash equilibrium solution of an optimal network formation tracking problem. A relative control error minimization technique is introduced to facilitate the formulation of a feasible infinite-horizon total-cost differential graphical game. A dynamic programming-based feedback-Nash equilibrium solution to the differential graphical game is obtained via the development of a set of coupled Hamilton–Jacobi equations. The developed approximate feedback-Nash equilibrium solution is analyzed using a Lyapunov-based stability analysis to demonstrate ultimately bounded formation tracking in the presence of uncertainties. In addition to control, this chapter also explores applications of differential graphical games to monitoring the behavior of neighboring agents in a network.