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Iterative Learning Control of Multi-agent Systems

The paper considers a group of systems (agents), each of which described by a model consisting from a linear part and a static nonlinearity, satisfying special quadratic constraints, connected by a feedback. All systems operate in the repetitive mode with a constant pass length, and with resetting to the initial state after each pass is complete. Data connections among the systems are defined 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 reaches a reference trajectory (pass profile) as the number of passes grows infinitely. The ultimate results are written in form of linear matrix inequalities. In linear case the consensus problem is reduced to simultaneous stabilization problem. An example of networked iterative learning control design for four identical gantry robots is considered based on models constructed using measured frequency response data.