Anurag Rai

Initial-Condition Estimation in Network Synchronization Processes: Algebraic and Graphical Characterizations of the Estimator

A graph-theoretic analysis of state inference for a class of network synchronization (or diffusive) processes is pursued. Precisely, estimation is studied for a nonrandom initial condition of a canonical synchronization dynamic defined on a graph, from noisy observations at a single network node. By characterizing the maximum-likelihood estimation of the initial condition and the associated Cramer–Rao bound, graph properties are identified (e.g., symmetries, interconnection strengths, spectral measures) that determine (1) whether or not estimation is possible and (2) the quality of the estimate.

Vulnerable links and secure architectures in the stabilization of networks of controlled dynamical systems

This work considers destabilization attacks acting on a single link in a systems logical interconnection structure. This structure, or signal architecture, is characterized by the causal relationships among exposed signals within a network of interconnected systems. The concept of a vulnerable link is thus characterized, and necessary and sufficient conditions for identifying vulnerable links are provided. The vulnerability of various system architectures are then characterized by the vulnerability of their weakest link, and it is shown that every transfer function has a completely secure architecture with no vulnerable links. A numerical example then illustrate these concepts with concrete architectures.

A convex optimization approach to decentralized rate control in wireless networks with partial interference

Because wireless networks use shared communication channels, contention and interference can significantly degrade throughput and fairness. Optimal rate control algorithms can be designed for wireless networks by modeling the contention between routers using capacity constraints and solving a convex optimization problem. In this work we develop a more accurate network model that directly incorporates partial interference as a receiving constraint, so that it is modeled separately from contention. We show that using this new model leads to a convex optimization problem when formulated using link rates, but it is non-convex when formulated using flow rates.We then use numerical results to illustrate situations when modeling partial interference separately yields significantly higher effective utilities in practical network topologies.

A Minimal Realization Technique for the Dynamical Structure Function of a Class of LTI Systems

The dynamical structure function of a linear time invariant (LTI) system reveals causal dependencies among manifest variables without specifying any particular relationships among the unmeasured states of the system. As such, it is a useful representation for complex networks where a coarse description of global system structure is desired without detailing the intricacies of a full state realization. In this paper, we consider the problem of finding a minimal state realization for a given dynamical structure function. Interestingly, some dynamical structure functions require uncontrollable modes in their state realizations to deliver the desired input-output behavior while respecting a specified system structure. As a result, the minimal order necessary to realize a particular dynamical structure function may be greater than that necessary to realize its associated transfer function. Although finding a minimal realization for a given dynamical structure function is difficult in general, we present a straightforward procedure here that works for a simplified class of systems.

Loop-Free Backpressure Routing Using Link-Reversal Algorithms

The backpressure routing policy is known to be a throughput optimal policy that supports any feasible traffic demand in data networks, but may have poor delay performance when packets traverse loops in the network. In this paper, we study loop-free backpressure routing policies that forward packets along directed acyclic graphs (DAGs) to avoid the looping problem. These policies use link reversal algorithms to improve the DAGs in order to support any achievable traffic demand. For a network with a single commodity, we show that a DAG that supports a given traffic demand can be found after a finite number of iterations of the link-reversal process. We use this to develop a joint link-reversal and backpressure routing policy, called the loop free backpressure (LFBP) algorithm. This algorithm forwards packets on the DAG, while the DAG is dynamically updated based on the growth of the queue backlogs. We show by simulations that such a DAG-based policy improves the delay over the classical backpressure routing policy. We also propose a multicommodity version of the LFBP algorithm, and via simulation we show that its delay performance is better than that of backpressure.