Adaptive model predictive control (MPC) robustly ensures safety while reducing uncertainty during operation. In this paper, a distributed version is proposed to deal with network systems featuring multiple agents and limited communication. To solve the problem in a distributed manner, structure is imposed on the control design ingredients without sacrificing performance. Decentralized and distributed adaptation schemes that allow for a reduction of the uncertainty online compatibly with the network topology are also proposed. The algorithm ensures robust constraint satisfaction, recursive feasibility and finite gain $ell_2$ stability, and yields lower closed-loop cost compared to robust distributed MPC in simulations.
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