Graph theory-based synchronization for stochastic uncertain complex dynamical networks via inverse optimal adaptive control

This paper is concerned with the synchronization of stochastic uncertain complex dynamic networks with time-varying delays. In contrast to existing synchronization network models, the current study considers both internal time-varying delays and coupling time-varying delays. By analyzing the two factors (i.e. time-varying delays and uncertainties) on the synchronization performance of stochastic uncertain complex dynamic networks, a new inverse optimal adaptive control is proposed. The analysis tool developed in this paper is based on Lyapunov technique, algebraic graph theory and inverse optimality, which does not need to solve Hamilton-Jacobi-Bellman equation. Some sufficient conditions are established for the synchronization of stochastic uncertain complex dynamic networks with time-varying delays. To demonstrate the effectiveness of the present approach, simulation results are illustrated.