Distributed and Constrained $\mathcal{H}_2$ Control Design via System Level Synthesis and Dual Consensus ADMM

Abstract

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, including future power systems with weather-dependent renewable generation. System level synthesis is a recent technique which has been used to reparametrize the optimal control problem as a convex program. However, prior work is restricted to a centralized control design, which 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 the previous optimal control problem, while incorporating agent-specific and globally coupled constraints in a non-conservative manner. 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