Iterative learning control design for multiagent systems based on 2D models

This paper considers a group of systems (agents) described by linear continuous or discrete models. All systems operate in the repetitive mode with a constant pass length, with resetting to the initial state after each pass is complete. Information exchange among the systems is described by a directed graph. The problem of reaching a consensus is formulated as designing an iterative learning control law (protocol) under which the output variable of each agent converges to a reference trajectory (pass profile) as the number of passes grows infinitely. This problem is solved using an original approach based on 2D models and a 2D modification of the vector Lyapunov function method. The ultimate results are written in form of linear matrix inequalities. 2D counterparts of the Fax–Murray theorem are established. An illustrative example is given.