NSF CNS-1739990: CPS: A Convex Framework for Control of Interconnected Systems over Delayed Networks
Recent years have seen an explosion in the use of cellular and wifi networks to deploy fleets of semi-autonomous physical systems, including 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 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 number of subsystems, and which, given models of the dynamics, communication links, and uncertainty, will return a controller which is: provably stable; robust to modeled 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 parameterize 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.
Matthew M. Peet (PI), Arizona State University
Morgan Jones (PhD), Arizona State University
Rushaub Tilati (MS), Arizona State University
M. M. Peet
SOS Methods for Multi-Delay Systems: A Dual Form of Lyapunov-Krasovskii Functional
Submitted to IEEE Transactions on Automatic Control.
[arXiv] [.pdf] [.ps] [related talk]
Summary: A new class of Lyapunov stability condition for systems with delay is proposed. The new class has additional structure and can be combined with feedback to create a convex approach to controller synthesis.
G. Maio and M. Peet and K. Gu
Inversion of Separable Kernel Operator and Its Application in Control Synthesis
in "Delays and Interconnections: Methodology, Algorithms and Applications", Springer, To Appear.
[arXiv] [.pdf] [.ps]
CDC/ACC Conference Publications:
G. Miao, M. Peet and K. Gu
Inversion of Separable Kernel Operators in Coupled Differential-Functional Equations and Application to Controller Synthesis
To appear at the IFAC World Congress. Toulouse, France. July 9-14, 2017.
[arXiv:1703.10253]] [.pdf] [.ps] [slides]
A Convex Reformulation of the Controller Synthesis Problem for MIMO Single-Delay Systems with Implementation in SOS
Proceedings of the American Control Conference. Seattle, WA. May 22-26, 2017..
[arXiv] [.pdf] [.ps] [slides]