  We will present a new general framework for robust and adaptive control that
allows for distributed and scalable learning and control of large systems of
interconnected linear subsystems. The control method is demonstrated for a
linear time-invariant system with bounded parameter uncertainties, disturbances
and noise. The presented scheme continuously collects measurements to reduce
the uncertainty about the system parameters and adapts dynamic robust
controllers online in a stable and performance-improving way. A key enabler for
our approach is choosing a time-varying dynamic controller implementation,
inspired by recent work on System Level Synthesis. We leverage a new robustness
result for this implementation to propose a general robust adaptive control
algorithm. In particular, the algorithm allows us to impose communication and
delay constraints on the controller implementation and is formulated as a
sequence of robust optimization problems that can be solved in a distributed
manner. The proposed control methodology performs particularly well when the
interconnection between systems is sparse and the dynamics of local regions of
subsystems depend only on a small number of parameters. As we will show on a
five-dimensional exemplary chain-system, the algorithm can utilize system
structure to efficiently learn and control the entire system while respecting
communication and implementation constraints. Moreover, although current
theoretical results require the assumption of small initial uncertainties to
guarantee robustness, we will present simulations that show good closed-loop
performance even in the case of large uncertainties, which suggests that this
assumption is not critical for the presented technique and future work will
focus on providing less conservative guarantees.
