A System Level Approach to Optimal Controller Design for Large-Scale Distributed Systems

Modern cyber-physical systems, such as the smart grid, software-defined networks, and automated highway systems, are large-scale, physically distributed, and interconnected. The scale of these systems poses fundamental challenges for controller design: the traditional optimal control methods are globally centralized, which require solving a large-scale optimization problem with the knowledge of the global plant model, and collecting global measurement instantaneously during implementation. The ultimate goal of distributed control design is to provide a local, distributed, scalable, and coordinated control scheme to achieve centralized control objectives with nearly global transient optimality. This dissertation provides a novel theoretical and computational contribution to the area of constrained linear optimal control, with a particular emphasis on addressing the scalability of controller design and implementation for large-scale distributed systems. Our approach provides a fundamental rethinking of controller design: we extend a control design problem to a system level design problem, where we directly optimize the desired closed loop behavior of the feedback system. We show that many traditional topics in the optimal control literature, including the parameterization of stabilizing controller and the synthesis of centralized and distributed controller, can all be cast as a special case of a system level design problem. The system level approach therefore unifies many existing results in the field of distributed optimal control, and solves many previously open problems. Our system level approach has at least the following four technical merits. First, we characterize the broadest known class of constrained linear optimal control problem that admits a convex formulation. Specifically, we show that the set of convex system level design problems is a strict superset of those that can be parameterized using quadratic invariance. Second, we identify a class of system level design problems, which we called the localized optimal control problems, that are scalable to arbitrary large-scale systems. In particular, the parallel synthesis and implementation complexity of the localized optimal controller are O(1) compared to the size of the networked system. Third, we provide a unified framework to simultaneously incorporate user-specified design specification on the closed loop and the hardware implementation constraints on the controller into the optimal controller design process. Lastly, we provide a system level approach that supports the co-design of optimal controller and its sensing and actuating architecture. We demonstrate the effectiveness of our method on a 51200-state randomized heterogeneous power network model, and show that the system level approach provides superior scalability over the centralized and distributed method. For such a large-scale example, the theoretical computation time for the centralized scheme is more than 200 days, and the distributed optimal control scheme is intractable. In contrast, it only takes 38 minutes to synthesize a localized optimal controller that achieves at least 99% global optimality guarantee.