Current Research and Projects

Control of Traffic Networks from Temporal Logic Specifications

We present a framework for controlling traffic networks to accomplish control objectives expressed using temporal logic. We investigate both networks of signalized intersections in which the control input is the traffic light signaling and freeway traffic networks in which the control input is metering rates at onramps. Temporal logic specifications for such networks include conditions such as:

By leveraging recently developed tools that apply techniques from formal methods to control synthesis for dynamical systems, we generate control policies that are guaranteed to satisfy complex objectives. In addition to suggesting a novel application domain for these powerful new synthesis tools, we demonstrate that the structural properties particular to flow networks such as traffic allow significant reduction in computation time. For example, freeway traffic networks can be faithfully modeled as polyhedral-partitioned, piecewise affine systems and thus efficient tools for polyhedral computation are used to find a finite state abstraction of the dynamics. Likewise, for signalized intersections, the dynamics of traffic queues and the resulting sparsity of queue interaction allows efficient computation of signal control policies that react to curent traffic conditions.

LTL Model

Learning-based Approaches to Control Synthesis of Probabilistic Systems from Temporal Logic Specifications

We consider the problem of controlling probabilistic systems, modeled as Markov Decision Processes, to achieve objectives expressed in linear temporal logic. We aim to bridge the gap between automata- and graph-theoretic techniques well-suited for verification and synthesis of nondeterministic systems and the statistical approaches for probabilistic systems primarily developed in the machine learning community. Our approach draws on results from, among other domains, probabilistic model checking, the theory of Markov chains, machine learning, and graph theory.

Grid World

A Compartmental Model for Traffic Networks and its Dynamical Behavior

We propose a general traffic network flow model particularly suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity (lack of congestion) as well as upstream demand of traffic wishing to flow through the junction. This approach is rooted in the celebrated Cell Transmission Model for freeway traffic flow. Unlike related results which rely on certain system cooperativity properties, our model generally does not possess these properties. We show that the lack of such properties is in fact a useful feature that allows traffic control methods, such as ramp metering, to be effective. Finally, we leverage these results to develop a linear program for optimal ramp metering.

Traffic Model

Switching Control Synthesis of Hybrid Systems for Safety

We investigate methods for synthesizing switching policies for networked dynamical systems that are capable of operating in various modes. Such hybrid systems often operate autonomously in each mode, and a supervisory controller switches between modes to guarantee certain criteria such as safety or performance. Applications include multiagent surveillance and ramp metering strategies for traffic networks.

Traffic Model

Safety Verification of Interconnected Systems

We present a sum-of-squares approach to verifying a state-based safety constraint of a network consisting of interconnected subsystems. We offer an approach that relies on the interconnection structure and equilibrium-independent input-output properties of the subsystems and therefore does not suffer from the shortcomings of related approaches such as an arbitrary parameterization of barrier functions or exact knowledge of the system equilibrium, which may be unknown for large systems.

Interconnected Systems

Previous Research

Formation Control with Size Scaling

We consider the problem of formation control of a team of mobile agents when only a subset of the agents know the desired size scaling of the formation. The remaining agents implement a cooperative control law using only local interagent position information such that the agents converge to the desired formation scaled by the desired size. The control laws that we design require only knowledge of relative displacement to neighboring agents, i.e. no communication among the agents. By allowing the size of the formation to change, the group can dynamically adapt to changes in the environment such as unforeseen obstacles, adapt to changes in group objectives, or respond to threats.

Formation Scaling

Pricing Design for Noncooperative Dynamic Games

We consider agents acting noncooperatively in a networked, dynamic game setting and seek to design appropriate incentives to close the gap between what is possible with cooperative control, and what happens in the noncooperative environment. We pose the problem as a convex optimization problem and demonstrate our approach theoretically in the setting of energy management in buildings, and future work will investigate methods for applying our approach to a building on the UC Berkeley campus.

Pricing Design

Data Mining Class Project: Predicting Supreme Court Justice Votes from Oral Arguments

The purpose of this course project is to predict the votes of US Supreme Court justices using oral argument transcripts. By analyzing the Justices' comments and questions posed to each arguing party, we are able to provide predictions as to how the justices will vote. See the project webpage here.

Supreme Court Prediction

NASA Jet Propulsion Laboratory, Guidance and Control Analysis Group

(Summer 2012)

During Summer 2012, I worked at NASA's Jet Propulsion Lab in Pasadena, CA. I researched primitive body navigation focusing on state estimation techniques for landing spacecraft on primitive bodies such as comets and asteroids. Primitive bodies pose unique challenges for guidance, navigation and control as they are often irregularly shaped, have irregular gravitational fields, and can outgas, introducing severe disturbances. Additionally, in contrast to larger astronomical bodies that are well-studied, useful information such as landmark features, exact positioning, and inertial data are largely unknown. I investigated methods for state estimation that incorporates data from a variety of sensors and is robust to outliers to allow sample return missions from these small bodies.

Undergraduate Research

Georgia Robotics and Intelligent Systems Lab

(2009–2010)

I participated in Georgia Tech's Undergraduate Research Option under the advisement of Dr. Magnus Egerstedt in the Georgia Robotics and Intelligent Systems Lab. My three-semester project culminated in an Undergraduate Thesis entitled "Size-Switching in Formation Control" which explores decentralized methods for allowing a team of mobile agents in formation to collectively change formation size while maintaining formation shape.

EcoCAR Competition

(2008–2010)

I was a member of the Georgia Tech EcoCAR team, working primarily on the supervisory control for our hybrid-electric vehicle. The EcoCAR competition was a three-year advanced vehicle technologies competition established by the US DOE. I created simulations of the vehicle using steady-state modeling of the major vehicle components and developed supervisory control strategies. I also organized and was a member of an EcoCAR senior design team to work on specific controls-related aspects of the vehicle design.

Georgia Tech Research Institute

(2007–2009)

I worked at the Georgia Tech Research Institute (GTRI) for four semesters in the Communications and Networking Division (CND) of the Information Technology and Telecommunications Laboratory (ITTL) as part of the Georgia Tech Cooperative Education program. My research focused on developing technologies to dramatically increase public safety communications interoperability and on creating statewide communications plans and operating procedures. I also spent time working on the Direct To Discovery Project, a project focused on connecting K-12 students to university-level research through high-definition, interactive video conferencing with professors and researchers.

Project Links

Class Project: Predicting Supreme Court Justice Votes from Oral Arguments
Undergraduate Thesis
Senior Design Project [External Link]