The control of arbitrary size networks of linear systems via graphon limits: An initial investigation

To achieve control objectives for extremely complex and very large scale networks using standard methods is a challenging, if not intractable, task. In this paper, we propose a novel way to approximately control network systems which lie in a sequence with a well defined limit by the use of graphon theory and the theory of infinite dimensional systems. The general controllability problem is analyzed for the infinite system and then the control performance in terms of the upper bound for the L
²
state error between the limit system and the sequence of network systems is given. Finally, an example of the application of the minimum energy control methodology for network systems with sampled weightings is demonstrated.