Modern cyber-physical systems (e.g. software-defined networks (SDN),smart-grid) are large-scale, distributed, interconnected, and dynamic. While layered control architectures are ubiquitous and arguably necessary for predictable and desirable behavior, there is no general theory that offers a principled approach to their design and/or to reverse-engineering their functionality. Motivated by SDN and human sensorimotor control, we argue that such a theory must incorporate layering, dynamics, optimization and control and highlight our recent progress in developing such a unified framework. In particular we show that by suitably relaxing an optimal control problem that jointly addresses determining and following an optimal trajectory, one can naturally recover a layered architecture composed of co-designed "reflex" and planning layers.
Building this "reflex" layer requires solving another co-design problem, namely that of jointly synthesizing an optimal distributed feedback controller and its required architecture (i.e., placement of sensors, actuators, and communication links between them) — the integration of these two tasks is required to explore the tradeoff between closed-loop performance (i.e. tracking and disturbance rejection) and architectural cost. We show that this challenge of co-design can be framed as one of seeking structured solutions to a linear inverse problem and formulate the Regularization for Design framework, in which we augment variational formulations of controller synthesis problems with convex penalty functions that induce a desired (sparse) controller architecture. The resulting regularized formulations are convex optimization problems that can be solved efficiently, and provide a unified computationally tractable approach for the simultaneous co-design of a structured optimal controller and the actuation, sensing and communication architecture required to implement it. Further, these problems are natural control-theoretic analogs of prominent approaches such as the Lasso, the Group Lasso, the Elastic Net, and others that are employed in structured inference. In analogy to that literature, we show that our approach identifies optimally structured controllers under a suitable condition on a "signal-to-noise" type ratio.
We conclude our talk with an application of these tools to SDN enabled high-frequency traffic control in wide area networks, and show the usefulness of our approach through simulation, emulation and experimental results. Time permitting, we will also make connections to recent neuroscience experiments.
Nikolai Matni is a postdoctoral scholar in Computing and Mathematical Sciences at the California Institute of Technology. He received the B.A.Sc. and M.A.Sc. in Electrical Engineering from the University of British Columbia, and the Ph.D. in Control and Dynamical Systems from the California Institute of Technology. His research interests broadly encompass the use of layering, dynamics, control and optimization in the design and analysis of complex cyber-physical systems; current application areas include software defined networking and sensorimotor control. His Ph.D. work focussed on foundational theory of distributed optimal control, and in particular on controller synthesis, architecture design and system identification. He was awarded the 2013 IEEE CDC Best Student-Paper Award.