Scalable system level synthesis for virtually localizable systems

In previous work, we developed the system level approach to controller synthesis, and showed that under suitable assumptions, this framework allowed for the synthesis of localized controllers. We further showed that such localized controllers enjoy O(1) synthesis and implementation complexity relative to the dimension of the global system, making them particularly well suited for the control of large-scale cyber-physical systems. However, the assumptions under which a system is localizable are stringent: roughly, a system is localizable if the controller has the necessary actuation, sensing and communication resources to “get out ahead” of the propagation of a disturbance and neutralize it, thus containing its effect to a localized spatiotemporal region. In this paper, we relax the assumption of exact localizability, and develop a controller synthesis methodology that is applicable to arbitrary systems that are in an appropriate sense “easy to control.” We focus on the state-feedback setting and develop a simple necessary and sufficient condition for robust stability using the system level approach. We then leverage this condition, along with the introduction of virtual actuation, communication and system responses into the synthesis process, to design stabilizing controllers that have (i) O(1) synthesis and implementation complexity and (ii) guaranteed performance bounds. We end with a power-inspired example demonstrating the usefulness of these techniques, wherein we synthesize a near globally optimal controller for a system that is neither localizable nor quadratically invariant.