Research interests

Our research focuses on graph dependent performance limitations in large-scale interconnected dynamical networks. The primary focus is on revealing foundational role of underlying structure/graph of large-scale dynamical networks. The underlying structure of a network depends on coupling structure among the subsystems, which are usually imposed by physical laws or global objectives. Our research results are applicable to several application areas: financial networks, smart energy networks, networks of autonomous vehicles, and biological networks.

Meta-population networks of 15 United States airport hubs with their normal, optimal, and robust traffic volume, respectively [link].
Monitoring and active-regulation of the air traffic volume is one potential intervention to decrease the negative effects of vaccine tourism.

Goal: Minimize Robot/RaceCar's deviation from desired trajectory:

• Maximize localization accuracy, by using on-board sensors.

• Generate appropriate control input, by using on-board actuators.

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Goal: Stabilize power grid using HVDC generators; place PMUs that make the grid observable

• Where to place few HVDCs and PMUs for actuation and sensing?

Internet-scale applications present several technical challenges. In this project, we investigate the performance analysis and synthesis of distributed system throttlers (DST). A throttler is a mechanism that limits the flow rate of incoming metrics, e.g., bytes per second, network bandwidth usage, capacity, traffic, etc. This can be used to protect a service’s backend/clients from getting overloaded, or to reduce the effects of uncertainties in demand for shared services. We study performance deterioration of DSTs subject to demand uncertainty. We then consider network synthesis problems that aim to improve the performance of noisy DSTs via communication link modifications as well as server update cycle modifications.

Goal: Minimize performance deterioration (e.g., over-throttling, mismatch, convergence rate).

• Finding the optimal update cycle for a DST.

• Generate appropriate control input, by using local and global information.

We propose new insights into the network centrality based not only on the network graph, but also on a more structured model of network uncertainties. I investigate several structures for noise input and provide engineering insights on how each uncertainty structure can be relevant in real world settings. Then, a new centrality index is defined in order to assess the influence of each agent or link on the network performance. Our results assert that agents or links can be ranked according to this centrality index, and their rank can drastically change from the lowest to the highest, or vice versa, depending on the noise structure. This fact hints at emergence of fundamental tradeoffs on network centrality in the presence of multiple concurrent network uncertainties with different structures. We also build on our results and extend them to consider the role of both time-delay and uncertainty structure in the centrality ranking.

A proper abstraction of a large-scale linear consensus network with a dense coupling graph is one whose number of coupling links is proportional to its number of subsystems and its performance is comparable to the original network. Optimal design problems for an abstracted network are more amenable to efficient optimization algorithms. From the implementation point of view, maintaining such networks are usually more favorable and cost effective due to their reduced communication requirements across a network. Therefore, approximating a given dense linear consensus network by a suitable abstract network is an important analysis and synthesis problem. In this paper, we develop a framework to compute an abstraction of a given large-scale linear consensus network with guaranteed performance bounds using a nearly linear time algorithm. First, the existence of abstractions of a given network is proven. Then, we present an efficient and fast algorithm for computing a proper abstraction of a given network. Finally, we illustrate the effectiveness of our theoretical findings via several numerical simulations.

In 2006, Xu conjectured that: for any 2-connected graph G of order n (n ≥ 2), its signed edge domination number is greater than or equal to one. In this project, we show that this conjecture is not true. More precisely, we show that for any positive integer m, there exists an m-connected graph G such that its signed edge domination number is less than or equal to − m/6 |V (G)|. Also for every two natural numbers m and n, we determine the signed edge domination number of the complete bipartite graph with part sizes m and n.

We develop some basic principles to investigate performance deterioration of dynamical networks subject to external disturbances. First, we propose a graph-theoretic methodology to relate structural specifications of the coupling graph of a linear consensus network to its performance measure. Moreover, for this class of linear consensus networks, we introduce new insights into the network centrality based not only on the network graph but also on a more structured model of network uncertainties. Then, for the class of generic linear networks, we show that the H2-norm, as a performance measure, can be tightly bounded from below and above by some spectral functions of state and output matrices of the system. Finally, we study nonlinear autocatalytic networks and exploit their structural properties to characterize their existing hard limits and essential tradeoffs.

The class of dynamical networks with autocatalytic structures can be found in most of the planet’s cells from bacteria to human, engineered, and economic systems. In an interconnected control system with autocatalytic structure, the system’s product (output) is necessary to power and catalyze its own production. There has been some recent interest to study models of the glycolysis pathway which is an example of an autocatalytic dynamical network in biology that generates adenosine triphospate (ATP) which is the cell’s energy currency and is consumed by different mechanisms in the cell. Other examples of autocatalytic networks include engineered power grids whose machineries are maintained using their own energy product as well as financial systems which operate based on generating monetary profits by investing money in the market. Recent results show that there can be severe theoretical hard limits on the resulting performance and robustness in autocatalytic dynamical networks. It is shown that the consequence of such tradeoffs stems from the autocatalytic structure of the system.

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Fractional-order systems, widely regarded as an extension of integer-order systems, are those dynamical systems whose state space representations involve non-integer derivatives of the states. In this project, we investigated important problems regarding fractional-order systems, which are their stability analysis, oscillation analysis, and chaos control.

‘‘In mathematics, a Golomb ruler is a set of marks at integer positions along an imaginary ruler such that no two pairs of marks are the same distance apart.” —wiki

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