Interplay between Network Topology and Stability of Control Systems with Delays

Northeastern University, Boston MA

Investigators

Abstract

Interplay between Network Topology and Stability of Control Systems with Delays Objective: Delays, ubiquitous in control systems, mainly arise from sensing, actuation and decision-making activities; and the topology describes which control systems are tied with each other via a network, as seen in coordination of autonomous vehicles, tele-operation, manufacturing enterprise systems and vehicular traffic flow dynamics. Through the same network, delays and topology affect each other and combine together to determine the network stability. The objective of this program is to explain the non-trivial connections between the topologies of networks and the stability mechanisms of these networks in the presence of multiple delays. Evident from the literature, there exists no general stability treatment for control systems with multiple delays, and this knowledge gap currently prevents the availability of explicit rules by which networks and their controllers can be designed for improved stability. Intellectual merit: The intellectual merit of this project is a new and unrecognized mathematical approach for the stability theory of multiple delay systems, which unlocks the aforementioned knowledge gap and will reveal thorough understanding of the amounts of delays different network topologies can withstand without loosing stability. The approach will lead to new rules with which networks, by design of their topologies, coupling strengths and controller gains, can be rendered more tolerant against delays. The new tools attained in this project will also be tested in mechatronics experiments and will put light on the transition of the new knowledge from small size networks to large size ones. The transformative aspects of the proposal are seen in the non-traditional approaches taken to enable (a) the stability analysis of multiple delay systems, (b) the explicit formulations that reveal the intertwined relationships between topology, delays and stability; (c) new paradigms for the parallel design of network topologies and controllers in the presence of multiple delays. Broader impacts: The broader impacts of the project are: (i) engineering education via outreach activities targeted to an audience including minorities and under-represented groups, and via advising undergraduate students in capstone design projects; (ii) enhancing research infrastructures via national and international collaborations; (iii) dissemination of results via a new tutorial-level web-site that will be developed to teach the analysis of delay systems; (iv) new results across disciplines including networked control systems, vehicular traffic flow, operations research and biology.