Suboptimal Solution of Nonlinear Graphical Games Using Single Network Approximate Dynamic Programming

In this paper, an online learning algorithm based on approximate dynamic programming is proposed to approximately solve the nonlinear continuous time differential graphical games with infinite horizon cost functions and known dynamics. In the proposed algorithm, every agent employs a critic neural network (NN) to approximate its optimal value and control policy and utilizes the proposed weight tuning laws to learn its critic NN optimal weights in an online fashion. Critic NN weight tuning laws containing a stabilizer switch guarantees the closed-loop system stability and the control policies convergence to the Nash equilibrium. In this algorithm, there is no requirement for any set of initial stabilizing control policies anymore. Furthermore, Lyapunov theory is employed to show uniform ultimate boundedness of the closedloop system. Finally, a simulation example is presented to illustrate the efficiency of the proposed algorithm.