  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.
