An Output Feedback Approach to Differential Graphical Games in Linear Multiagent Systems

This letter presents an output feedback approach to distributed optimal formation control of linear time-invariant multiagent systems. The formation control problem is formulated as a differential graphical game problem. It is assumed that each agent receives partial error-states of its immediate neighbors. To account for the dependence of the value function of each agent on the error-states of its extended neighbors, a robust observer that estimates the error-states of the extended neighbors using partial error-states of the immediate neighbors is designed. The observer is integrated with a controller to approximate a global feedback Nash equilibrium (FNE) solution of the differential graphical game. Stability of the closed-loop system and convergence of the estimated value functions to the approximate FNE solution are established using a Lyapunov-based analysis. Simulations demonstrate the efficacy of the developed approach.