We consider the task of designing sparse control laws for large-scale systems
by directly minimizing an infinite horizon quadratic cost with an β1β
penalty on the feedback controller gains. Our focus is on an improved algorithm
that allows us to scale to large systems (i.e. those where sparsity is most
useful) with convergence times that are several orders of magnitude faster than
existing algorithms. In particular, we develop an efficient proximal Newton
method which minimizes per-iteration cost with a coordinate descent active set
approach and fast numerical solutions to the Lyapunov equations. Experimentally
we demonstrate the appeal of this approach on synthetic examples and real power
networks significantly larger than those previously considered in the
literature