CPS: Small: A Convex Framework for Control of Interconnected Systems over Delayed Networks

Abstract: Recent years have seen an explosion in the use of cellular and wifi networks to deploy fleets of semi-autonomous physical systems, including unmanned aerial vehicles (UAVs), self-driving vehicles, and weather stations to perform tasks such as package delivery, crop harvesting, and weather prediction. The use of cellular and wifi networks has dramatically decreased the cost, energy, and maintenance associated with these forms of embedded technology, but has also added new challenges in the form of delay, packet drops, and loss of signal. Because of these new challenges, and because of our limited understanding of how unreliable communication affects performance, the current protocols for regulating physical systems over wireless networks are slow, inefficient, and potentially unstable. In this project we develop a new computational framework for designing provably fast, efficient and safe protocols for the control of fleets of semi-autonomous physical systems. The systems considered in this project are dynamic, defined by coupled ordinary differential equations, and connected by feedback to a controller, with a feedback interconnection which has multiple static delays, multiple time-varying delays, or is sampled at discrete times. For these systems, we would like to design optimal and robust feedback controllers assuming a limited number of sensor measurements are available. Specifically, we seek to design a class of algorithms which are computationally efficient, which scale to large numbers of subsystems, and which, given models of the dynamics, communication links, and uncertainty, will return a controller which is provably stable, robust to model uncertainty, and provably optimal in the relevant metric of performance. To accomplish this task, we leverage a new duality result which allows the problem of controller synthesis for infinite-dimensional systems to be convexified. This result allows the problem of optimal and robust dynamic output-feedback controller synthesis to be reformulated as feasibility of a set of convex linear operator inequalities. We then use semidefinite programming to parametrize the set of feasible operators and thereby test feasibility of the inequalities with little to no conservatism. In a similar manner, estimator design and optimal controller synthesis are recast as semidefinite programming problems and used to solve the problems of sampled-data and systems with input delay. The algorithms will be scalable to at least 20 states and the controllers will be field-tested on a fleet of wheeled robotic vehicles.