My work lies at the intersection of Network Science, Control, Communications, and Distributed Algorithms.

• What is Control Theory?

In particular, my research focuses on the analysis of dynamics on large-scale networks. These networks are prevalent in both the natural world (e.g., genetic networks, ecological networks, social networks), and in engineered applications (e.g., the Internet, the power grid, industrial control networks, large robotic swarms). In these settings, it is essential for the overall system to be resilient to components that behave in unanticipated, incorrect, or malicious ways. Understanding the behaviour of these complex systems requires us to consider both the network topology (i.e., who interacts with whom), and the network dynamics (i.e., what happens when two nodes interact). The confluence of complex network topologies, dynamics, and unreliable agents presents new and exciting challenges for researchers to tackle. Drawing from diverse disciplines, I develop novel and mathematically rigorous techniques for designing reliable networks of dynamical systems.

Current and Past Research Projects

Robustness and Resilience of Information Diffusion Dynamics in Complex Networks

Consider an arbitrary network of interconnected agents where each agent has some value, and the objective is to enable a subset of the agents to calculate some function of these values in a distributed manner. This scenario arises in a multitude of settings:

• A sink node in a sensor network might be tasked with computing the average measurement value of all the sensors
• A set of mobile robots might wish to communicate with each other in order to maintain a consistent formation
• A pollster in a social network might want to determine the opinion of the population on a certain topic.

Each agent interacts with its neighbors in the network, and the dynamics of these local interactions lead to global behaviour. Our work studies the interplay between these dynamics and the topology of the network to infer properties of the resulting system-wide behaviour, particularly with respect to small populations of agents that wish to affect the system functionality in some way.

One of our focal points has been the analysis and design of linear iterative strategies to enable information diffusion in networks. In these strategies, each agent repeatedly updates its value to be a weighted linear combination of its own previous value and those of its neighbors; such strategies have received a great deal of attention in the control systems community for the purpose of reaching asymptotic consensus (whereby all of the agents converge to the same value after an infinite number of iterations). Our work has shown that, despite their simplicity, these linear iterative strategies are substantially more powerful than previously recognized. Using concepts from linear system theory and structured system theory, we demonstrate that such strategies actually allow any agent in the network to obtain the values of any other agent after a finite number of iterations, thereby allowing any agent to calculate any arbitrary function of the initial values. Furthermore, even if a set of agents conspiratorially decide to spread misinformation about the values of other agents, our analysis reveals that linear iterative strategies provide every agent in the network with sufficient information to overcome this disruptive behavior (as long as the underlying network topology satisfies some fundamental conditions).

Our work also identifies topological (graph-theoretic) properties of networks that make them robust and resilient to perturbations and adversarial behaviour. In the context of information diffusion mechanisms, we use tools from random graph theory to analyze the robustness of large-scale complex networks. For example, our results have shown that various common random graph models possess a much richer structure than previously identified, and exhibit a thresholding behavior for a property that we term robustness, allowing them to diffuse information reliably in the presence of adversaries.

Part of our work in this area has been supported by the Waterloo Institute for Complexity and Innovation.

The Wireless Control Network

The advent of low-cost and reliable wireless networks holds great promise for large, spatially distributed industrial control systems. These networks allow sensor measurements of plant variables to be transmitted to controllers and plant operators without the need for excessive wiring, thereby yielding gains in efficiency and profitability for the operator. While the wireless nodes in these networks are typically low-power and battery operated, they also have some limited computational capability. In this project, we ask the question: can we utilize the collective computational capability available in the network to calculate the required feedback control laws? To answer this question, we introduce the concept of a Wireless Control Network (WCN) where the entire network itself acts as the controller - this is opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller.

The WCN introduces very low computational and communication overhead to the nodes in the network and allows the use of simple transmission scheduling algorithms. Since the WCN does not rely on the existence of dedicated controllers and inherently captures the case of nodes exchanging values with the plant at various points in the network, it can be used for plants with multiple sensing/actuation points connected to a multi-hop network. This makes WCNs suitable as a means for control of geographically distributed plants (e.g., building control, industrial process control). Furthermore, the WCN enables compositional design, where the existing wireless infrastructure can be easily extended to handle new plants that are brought online in the vicinity of the network. Finally, the utilized linear iterative scheme allows identification of malicious behavior by examining the transmissions of only a subset of the nodes in the network (provided that the network topology satisfies certain conditions).

This is a joint project with Miroslav Pajic, Rahul Mangharam and George Pappas at the University of Pennsylvania. For more details, see: http://www.seas.upenn.edu/~pajic/research/wcn.html

Resilient Control Systems

The central role that control systems play in a multitude of life-critical applications (from nuclear plants, power grids and manufacturing to aerospace systems and transportation) necessitates that they operate in a reliable and secure manner. Traditional control system security measures based on air-gaps and safety-through-obscurity are no longer sufficient, as control networks become increasingly connected to corporate backbones and utilize off-the-shelf components. The recent sophisticated intrusion of microcontrollers in nuclear plants by the Stuxnet worm is a prime example of the vulnerability of control systems to attacks. Furthermore, in contrast to traditional information technology systems, control systems present unique challenges for security because they interact with (potentially unstable) physical processes, requiring strict real-time guarantees.

Our research focuses on methods to analyze dynamical systems for vulnerabilities. We have developed analysis techniques based on structured system theory, which provides powerful tools to understand the interdependencies between system states, inputs and outputs. In turn, this allows us to identify critical components of the system that are vulnerable to attack, and thereby develop strategies to increase the resilience of the system.

This work was supported by a Discovery grant from NSERC.