Localized LQR control with actuator regularization

In previous work, we posed and solved the localized linear quadratic regulator (LLQR) problem - a LLQR controller is one that limits the propagation of dynamics to user-specified subsets of the global system. The advantages of taking this approach are tangible, as we show that this allows the controller to be synthesized and implemented in a scalable local manner. Implicit in this previous work was the existence of a feasible spatio-temporal constraint on the controller and closed loop response of the system that enforced these locality properties. This paper proposes and analyzes a procedure for designing such a spatio-temporal constraint, which can be interpreted as a measure of the implementation complexity of a controller, and a sparse actuation architecture that ensures that it is feasible. We show that the computational tasks involved can be suitably decomposed and solved using the alternating direction method of multipliers (ADMM), thus providing a scalable approach to designing a LLQR controller with a sparse actuation architecture.