  Design of optimal distributed linear feedback controllers to achieve a
desired aggregate behavior, while simultaneously satisfying state and input
constraints, is a challenging but important problem in many applications.
System level synthesis is a recent technique which has been used to
reparametrize the optimal control problem as a convex program. Prior work on
system level synthesis with state and input constraints has included
closed-loop finite impulse response and locality constraints or, in the case
where these constraints were lifted using a simple pole approximation, only a
centralized design was considered. However, closed-loop finite impulse response
and locality constraints cannot be satisfied in many applications. Furthermore,
the centralized design using the simple pole approximation lacks robustness to
communication failures and disturbances, has high computational cost and does
not preserve data privacy of local controllers. The main contribution of this
work is to develop a distributed solution to system level synthesis with the
simple pole approximation in order to incorporate state and input constraints
without closed-loop finite impulse response or locality constraints, and in a
distributed implementation. To achieve this, it is first shown that the dual of
this problem is a distributed consensus problem. Then, an algorithm is
developed based on the alternating direction method of multipliers to solve the
dual while recovering a primal solution, and a convergence certificate is
provided. Finally, the method's performance is demonstrated on a test case of
control design for distributed energy resources that collectively provide
stability services to the power grid.
