I am a reseracher in the advanced controls team at PNNL. I am also associated with the "Control of Complex Systems Initiative" (CCSI) at the lab.
My research interests are in developing efficient algorithms for automated decision making in complex physical, cyberphysical and social systems. In this effort,
I draw on tools from a variety of disciplines including stochastic control theory, convex and nonlinear optimization,
game theory, economics and machine learning. In recent years, I have focussed on challenging problems arising in large scale infrastructure systems.
Here is a recent CV .
Click on the topics below to see highlights from my recent research (click to expand). A comprehensive list of papers is available here .
Robustness of infrastructure networks
Most infrastructure networks (including the power grid, water and natural gas distribution networks) can be described as dynamical systems with nonlinear dynamics and uncertain inputs (
(for example, wind and solar forecast errors in the power grid). A natural first step towards understanding these stochastic nonlinear systems is to study their equibria: These are typically
solutions to some nonlinear system of equations $F(x)=s$ where $ x $ denotes the physical state variables (voltages or pressures, for example) and $ s $ denotes the inputs
(power generation/consumption at all nodes in the power grid). There are typically engineering constraints on the state variables $ x \in X$ and hence it is of interest to understand whether the
system $F(x)=s$ has a solution with $x \in X$ ($X$ can denote minimum/maximum voltage/pressure levels for example). Since $F$ is a nonlinear map, this is typically a difficult problem (determining existence of a solution to a system of nonlinear equations within a certain set)
and, unsurprisingly, is NPhard in general.
However, for real phyiscal systems, there is additional structure to both $F$ and $X$ that can be exploited to solve these problems efficiently. We develop an approach to solve $F(x)=s,x \in X$
given $s$, under certain conditions that are satisfied often for real power systems
[1][2]. Further, we address the robust solvability problem: Given a set $\mathcal{U}$ (arising from wind or solar generation forecast errors in a power grid, for example),
we want to determine whether for each $s \in \mathcal{U}$, there is a solution to $F(x)=s,x \in X$. Equivalently, we want to certify that
$$\mathcal{U} \subseteq \mathcal{F}=\{s: \exists x \in X, F(x)=s\}$$
We develop sufficient conditions for certifying this containment (based on polytime convex optimization algorithms) in
[3],
[4]. As opposed to previous work
on convex relaxations of the AC power flow equations, this approach produces inner approximations of the power flow feasibility set. This is of significant interest particularly in emergency situations (for example, close to a blackout) when
finding a feasible solution quickly is important.
 K. Dvijotham, M. Chertkov, and S. Low, “A differential analysis of the power flow equations,” in 2015 54th IEEE Conference on Decision and Control (CDC), 2015, pp. 23–30.
 K. Dvijotham, “Systems of quadratic equations: Efficient solution algorithms and conditions for solvability,” in 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2015, pp. 1027–1031.
 K. Dvijotham and K. Turitsyn, “Construction of power flow feasibility sets,” ArXiv eprints, Jun. 2015.
 K. Dvijotham, S. Low, and M. Chertkov, “Solving the power flow equations: a monotone operator approach,” ArXiv eprints, Jun. 2015.
Graphical models for infrastructure network analysis
Graphical models have proven to be a powerful tool in machine learning and artificial intelligence  they are a means to
compactly represent high dimensional probability distributions and reason about them efficiently. We show how to use graphical models to derive efficient approximation algorithms for the mixedinteger nonlinear optimization problems arising in power distribution networks
[1].
We also apply the same framework to study the market power of aggregators (companies that provide servies to the power grid by exploiting the demandside flexibility of a set of customers)
[2].
 N. Azizan Ruhi, K. Dvijotham, N. Chen, and A. Wierman, “Opportunities for Price Manipulation by Aggregators in Electricity Markets,” ArXiv eprints.

Best Student Paper Award, GREENMETRICS workshop at ACM SIGMETRICS
 PDF
 K. Dvijotham, M. Chertkov, P. Van Hentenryck, M. Vuffray, and S. Misra, “Graphical models for optimal power flow,” Constraints, pp. 1–26, 2016.

Best Paper Award, International Conference on Principles and Practice of Constraint Programming (CP 2016)
 PDF
Incentive driven dynamics in markets
Fisher markets are a simple model of exchange markets that have received a lot of attention in the computer science literature on algorithmic game theory. One of the recent celebrated
results from algorithmic game theory include combinatorial algorithms for computing market equilibria in Fisher markets. In parallel, there is a long history of work in the economics
literature addressing various price update dynamics that converge to market equilibria in Fisher markets (and more general markets). However, most of these price update rules do not have a
rational justification  ie, there is no explanation for why participants in an actual market would follow them. In recent work, I proved that under certain assumptions, a very natural set of
rationally justified price update dynamics converge to equilibria in Fisher markets. THe dynamics we consider are based on recursive belief formation (a merchant thinks about what other merchants might do, and
what they might in turn think about other merchants, etc.). For a very general notion of the belief formation procedure, we show that the market dyanmics based on price updates computed using these
beliefs are guaranteed to converge to the market equilibirum at a fast rate (which can be quantified)
[1]
 K. Dvijotham, Y. Rabani, and L. Schulman, “Convergence of incentivedriven dynamics in Fisher markets,” in Proceedings of the TwentySeventh Annual ACMSIAM Symposium on Discrete
Algorithms, SODA 2017, Barcelona, Spain, January 1012, 2017, 2017, pp. 2039–2052.