To achieve control objectives for dynamical systems distributed over extremely complex and very large scale networks using standard methods is an intractable task. In this work we propose a novel way to approximately control such network systems when they lie in a sequence of networks with a well defined limit in the sense of graphon theory. In particular, this yields a methodology which can be applied to the minimum energy state to state control problem for dynamical systems interacting over complex large scale networks. In this talk it will be explained how first the problem is solved for the limit system by the application of infinite dimensional linear control system theory. This then yields a centralized feedback control law whose finite approximations give control laws for the complex networked systems in the sequence under consideration. The crucial features of this procedure are that (i) each of the steps is computationally feasible and (ii) the method gives upper bounds for the difference between the state trajectories of the limit system and the associated finite network systems. Furthermore, the same overall methodology is effective for the corresponding linear quadratic regulator problem. Finally, a computational example will be presented in the talk together with some observations concerning the decentralized control of complex networks.
Welcome to everyone!