Learning distributed tracking protocol for LPV multi-agent systems from noisy data

This paper investigates the output tracking problem for unknown linear parameter-varying multi-agent systems (LPV MASs) operating over jointly connected switching networks. The design of distributed data-driven tracking controllers depends on time-varying output regulator equations. However, disturbances and scheduling signals make exact regulator-equation solutions difficult to obtain. To handle this difficulty, approximate solutions are searched over system sets that are compatible with the available dataset. A data-driven optimization problem is then established to minimize output regulator error matrices and compute approximate solutions. To improve the accuracy of these approximate solutions, two learning strategies are developed: (i) an iterative scheme that sequentially incorporates multiple datasets into the optimization process and (ii) an active learning scheme that strategically selects data points to reduce the compatible system sets and refine the solutions. The stability analysis proves that all tracking errors are ultimately uniformly bounded (UUB) under the resulting protocol. Simulation results further demonstrate the effectiveness of the proposed data-driven methods.