
Brief
Summary:
My main
expertise is in
the broad area
of control
systems,
networks, power
systems, and
optimization. In
the past two
years, my
research has
been focused on
the optimization
techniques
specialized for
energy systems
with the aim of
solving hard
nonconvex
problems, such
as the
50yearold
optimal power
flow problem. In
the 4 previous
years, my
research was to
apply control
and optimization
theory to
related
interdisciplinary
applications in
communications,
circuits,
networks, and
computer
science.
Specific results
include: (i)
convexification
of the optimal
power flow
problem, (ii)
smart antenna
design for
wireless
communication,
(iii) optimal
design of very
largescale
circuits, (iv)
design of
optimal
transmission
protocols for
internetworks,
(v) distributed
averaging
(consensus)
under
communication
constraints, and
(vi) a variety
of fundamental
control problems
such as
decentralized
control of
interconnected
systems and
biologically
motivated
controller
design. (back
to the top)

Smart Grid:
Over the
past few years, the idea of upgrading today's
transmission grid into a Smart Grid has been
seriously considered by the electric power
industry, state and federal regulators,
government agencies, and academics. At the high
level, the goal is to modernize the electricity
transmission and distribution system to maintain
a reliable and secure electricity infrastructure
that can meet future demand growth. In
particular, a smart grid must have many
properties, including: (i) optimized efficiency,
reliability, and flexibility, (ii) the ability
to integrate distributed (renewable) resources
and distributed generation, and (iii) the
capability to interact with plugin hybrid
electric vehicles. From the system point of
view, the deign of a smart grid requires several
tools and theories from various areas of
mathematics and engineering.
All of the areas that I have
worked on fit within a multifaceted,
interdisciplinary approach to the problem of
designing a smart grid:

Optimization: According
to a National Science Foundation
report, one of the three
important actions needed to be
taken towards designing a smart
grid is to create new
optimization methods that can
solve the existing nonconvex
problems associated with power
grids.

Control: The
controllers used in the existing
conventional grids are mainly
based on the centralized control
theory. However, a truly
decentralized and robust
controller is needed for a smart
grid with extensive use of small
distributed generators and
active load control.

Communications: Meters,
appliances, consumer devices and
plugin hybrid electric vehicles
must be made ``smart," meaning
that they should be able to
communicate with each other and
with the grid. Wireless
communication theory plays an
important role in deciding what
type of communication means
suits the needs of a smart grid.

Networks: More
generally, internetworking plays
a fundamental role in devising a
communication protocol (e.g.
TCP/IP and extensions) that
specifies how much information
each smart device should
exchange with the rest of the
grid and how the required amount
of information can be shared in
the network while minimizing
channel usage.

Computer Science: The
signals transmitted to the local
controllers of the grid by smart
devices are noisy, lossy and
asynchronous. To deal with this
issue, ideas from computer
science, such as consensus, need
to complement those from control
and optimization.
(back to
the top)
Electric Power Networks:
There are several
important optimization problems for a power
network, from resource allocation to state
estimation and different scheduling problems.
Since the behavior of a power network is
governed by nonlinear physical laws, these
optimization problems are nonconvex and hard to
solve. I have done a series of projects to show
how the physics of a power network helps design
efficient optimization algorithms.
Project 1: Optimal Power
Flow Problem
A fundamental optimization
problem for a power network is the resource
allocation problem, which is called optimal
power flow (OPF). This problem aims to find an
optimal operating point of a power network that
satisfies certain constraints on power and
voltage parameters and, in addition, minimizes
an appropriate cost function such as generation
cost or transmission loss. Since 1962, the OPF
problem has been extensively studied in the
literature and numerous gradient and nonlinear
algorithms have been proposed to find a
nearoptimal solution of this highly nonconvex
problem. Due to this nonconvexity, these
algorithms are not robust, lack performance
guarantees, and may not find a global optimum.
These issues become more critical for smart
grids consisting of many (distributed)
generators where the problem may need to be
solved frequently due to the fast timevarying
nature of renewable resources. Among many
optimization methods that have been adapted for
the OPF problem are linear programming,
quadratic programming, nonlinear programming,
Lagrange relaxation, interior point methods,
artificial intelligence, artificial neural
network, fuzzy logic, genetic algorithm,
evolutionary programming and particle swarm
optimization.
Our goal in this project
was to find a globally optimal solution of the
OPF problem in polynomial time using convex
optimization. To this end, we first derived the
dual of a variant of the OPF problem and
expressed it in the form of a semidefinite
program. Then, we proposed an easytocheck
condition under which the duality gap is zero so
the solution of the OPF problem can be recovered
from that of its convex dual problem. We showed
that this zerodualitygap condition is
satisfied for all IEEE test systems with 14, 30,
57, 118 and 300 buses, in addition to many
randomly generated systems. We investigated this
condition and showed that it holds widely in
practice. The main underlying reason for the
successful convexification of the OPF problem
can be traced back to the passivity of
transformers and transmission lines.
Project 2:
SecurityConstrained Optimal Power Flow Problem
The securityconstrained OPF
(SCOPF) problem aims to find an optimal
operating point of the grid that does not shift
the operation of the system to a critical state
if a fault happens. In order to design a
reliable smart grid, the SCOPF problem must be
solved in real time, yet it is known that the
SCOPF problem is even (much) harder than the OPF
problem. We have shown that the earlier OPF
result can also be generalized to this case as
well.
Project 3: Network
Topology Design
Given a power network, the
objective of this project was to study how the
topology of the network can be manipulated by
some nonlinear power electronic devices in such
a way that every OPF problem becomes solvable in
polynomial time over the same power circuit. In
this work, we proved that adding multiple
controllable phase shifters to certain lines of
the power network simplifies the verification of
the duality gap. In particular, if a sufficient
number of phase shifters are added to the
network, the duality gap becomes zero for the
OPF problem with nonlinear phase shifters. This
result implies that every network topology can
be modified by the integration of phase shifters
to guarantee the solvability of OPF in
polynomial time for all possible values of loads
and physical limits.
Project 4:
Electricity Market
This project was concerned
with the existence of competitive equilibria in
electricity markets with nonconvex network
constraints and nonlinear cost/utility
functions. We derived a necessary and sufficient
condition for the existence of a competitive
equilibrium in the context of economic dispatch.
We showed that a competitive equilibrium may
exist, even when the duality gap is nonzero for
the optimal power flow (OPF) problem. However,
the Lagrange multipliers for the power balance
equations in the OPF problem are indeed a
correct set of marketclearing prices in
presence of no duality gap. Moreover, we proved
that every power network can be manipulated by
phase shifters to guarantee the existence of a
competitive equilibrium.
Project 5: Feasible
Injection Regions of Power Networks
The goal of this project
was to understand the geometrical
properties of the injection region of a
treeshaped power network. We have characterized
the faces of the feasible injection region and
have shown that this highly nonconvex region
preserves important properties of a convex set
to the extent that optimizations over this
region can be cast as convex programs. More
precisely, we have focused on the Pareto front
of the injection region, i.e., the set of those
points in the injection region that are eligible
to be a solution to a typical OPF problem.
Although the injection region is still
nonconvex, we have proved that the Pareto
fronts of this set and its convex hull are
identical under some common constraints,
provided a practical angle condition is
satisfied. This implies that the injection
region can be replaced by its convex hull in the
OPF problem without changing the global
solution.(back
to the top)
Project 1: Synthesis of
LargeScale Linear Circuits
using Convex Optimization
Several important problems in
circuits, electromagnetics, and
optics can be reduced to the
analysis and synthesis of some
linear systems in the frequency
domain. These systems, in the
circuit theory, consist of
passive elements including
resistors, inductors,
capacitors, ideal transformers,
and ideal gyrators. Many methods
have been proposed in the
literature of automated circuit
synthesis to design the topology
and/or the component sizes of a
circuit, which can be broadly
classified as (i)
knowledgebased methods, (ii)
sizingbased methods, (iii)
sized topology generation
methods. These generalpurpose
techniques mainly rely on some
heuristic or local search
algorithms.
In this project, the objective
was to show that advanced
techniques in convex
optimization theory can be
exploited to globally optimize a
special, nonetheless important,
class of circuits efficiently
using a deterministic
polynomialtime algorithm. We
considered a linear multiport
network for which certain
specifications must be satisfied
at a desired frequency by
designing some elements of the
circuit. These unknown elements
are collected together in a
control unit. We showed that
designing a control unit in the
form of a switching network that
makes the circuit meet the
design specifications is an
NPcomplete problem. Instead,
the design of a passive network
for the control unit can be cast
as a semidefinite optimization.
Since a passive network may
require many components for its
implementation, the design of a
sparse (decoupled) passive
controller was also studied.
We elucidated the efficacy of
our work by designing optimal
radiating circuits corresponding
to antenna systems. As an
example, for the first time, we
have designed a wavelengthsize
onchip passive antenna system
with only one active element
(antenna element) that can make
simultaneous nulls in many
directions. This antenna design
can be computed in a few seconds
(rather than the weeks for
previous algorithms on onchip
antenna design). The radiation
pattern of this antenna is
comparable to the pattern of an
array smart antenna whose size
is more than 15 times the signal
wavelength.
Project 2:
Design of Passively Controllable
Smart Antennas
Conventional antennas for
wireless transmission, e.g. omnidirectional
antennas, radiate in almost all
directions. To avoid cochannel
interference, save power and
improve security, much attention
has been paid to designing smart
transmitting/receiving antenna
systems that can steer the beam
towards a desired direction and
made a null in undesired
directions. Array antenna is the
first type of smart antenna
whose size could be several
multiples of the signal
wavelength. An array antenna is
easy to program, but cannot be
easily implemented on a chip
partly due to its size. An
onchip smart antenna is the
second type of smart antenna
whose size is comparable to the
wavelength, but its programming
is a hard nonconvex problem.
Using the results developed in
Project 1, we designed a secure,
powerefficient, beamsteerable
and onchip transmission system
for wireless networks. Indeed,
we proposed a passively
controllable smart (PCS) antenna
system that can be programmed to
generate different radiation
patterns at the far field by
adjusting its variable passive
controller at every signal
transmission. Based on combining
theories from convex
optimization and algebraic
geometry, we showed that a PCS
antenna has excellent features.
Unlike the existing smart
antennas whose programming leads
to an NPhard problem or are
made of many active elements,
our PCS antenna has a
lowcomplex programming
capability and consists of only
one active element.
(back to
the top)
Communication
Networks:
There has been a growing interest in studying
the Internet congestion control ever since the
first congestion collapse occurred. The main
idea behind the existing congestion control
algorithms is more or less the same: each user
measures some feedback signal, such as packet
loss or queueing delay, and accordingly adapts
its transmission rate. Among the current
transmission control protocols (TCP) for
congestion control are TCPTahoe, Reno, New
Reno, and Vegas. From a mathematical standpoint,
the available resource allocation algorithms,
such as the primal, dual and primal/dual
algorithms, are particularly designed to solve
the underlying problem in a distributed way
asymptotically. Nonetheless, it is not clear how
well the network operates during the transient
time. For instance, the capacity link
constraints can be violated in this period.
Project 1:
Network Congestion Control Design via Optimal
Control Theory
The main motivation of this
project was that the available resource
allocation controllers are mainly devised to
derive the state of the system to a desired
equilibrium point and, therefore, they are
oblivious to the realtime behavior of the
closedloop system. In this work, we studied
what utility functionals (as opposed to utility
functions) the existing congestion control
algorithms maximize. In particular, we showed
that there exist meaningful utility functionals
whose maximization leads to the celebrated
primal, dual and primal/dual algorithms. This
idea opens up the possibility of designing
optimal transmission protocols to guarantee the
realtime performance of the network, something
which can never be realized by the existing
congestion controllers. Another big advantage of
our technique is that the designed protocol is
automatically stable, implying that the
stability of the algorithm is no longer an
issue.
Project 2:
Design of Congestion Controllers with
Satisfactory RealTime Performance
Motivated by the poor performance of congestion
control protocols based on only implicit
feedback from a high speed network, we studied
how to design a highperformance congestion
controller when it is allowed to receive
explicit information from the network. The
existing congestion control algorithms using
explicit feedback, such as the primal/dual
controller, cannot guarantee a desirable
performance at all times for the network and are
concerned with only the steadystate properties
of the system. To remedy this issue, we
introduced a new congestion control protocol
that has a tuning parameter whose adjustment
controls four important aspects of the realtime
performance of the network. (back
to the top)
Biologically
Motivated Controller Design:
Many theories have been developed for the
analysis and synthesis of timedelay control
systems due to the ubiquity of communication,
computation or propagation delays in both
embedded systems and biological circuits. Most
of the existing controller design methods for
timedelay systems regard delay as a nuisance
and design a controller for the undelayed model
of system in such a way that it is sufficiently
robust to the underlying delay. Nevertheless, it
is known that the voluntary introduction of
delay in the control of an undelayed system can
benefit the control process.
Transmission lines and
cavity delay lines (trombone delay lines)
play the role of delay blocks in
electronics/communications and optics,
respectively. Moreover, neurons and gene
regulatory networks are two sources of delays in
biology. Time delays appear in genetic networks
due to transcription, translation, and
translocation processes. Recently, there
has been a considerable amount of interest in
synthetic biology, whose goal is to build
artificial biological systems for engineering
applications. By regarding a biological
system composed of several interacting
components as a distributed control system, two
easytomanipulate parameters for design
purposes are (i) the topology of the distributed
system (interaction topology) and (ii) time
delays in the interactions. Hence, the
interaction graph together with the amount of
delays in the interactions plays the role of the
controller in a biological system.
Project 1: DelayBased
Controller Design for ContinuousTime Systems
Motivated by the
availability of different types of delays in
embedded systems and biological circuits, in
this project we studied the benefits that delay
can provide in simplifying the implementation of
controllers for continuoustime systems.
Given a continuoustime linear timeinvariant
(LTI) controller, we showed that the controller
can be approximated arbitrarily precisely by a
simple delaybased controller. This controller
is composed of some delay blocks, a few
integrators and possibly a unity feedback. This
result implies that every highorder LTI
controller has a simple delaybased
implementation, which uses delay blocks rather
than several integrators. Different
problems associated with the approximation
procedures, such as finding the optimal number
of delay blocks or studying the robustness of
the designed controller with respect to delay
values, were then investigated. We also studied
the design of an LTI continuoustime controller
satisfying given control objectives whose
delaybased implementation needs the least
number of delay blocks.
To
demonstrate the importance of our results, we
showed that the slow dynamics of a gene
regulatory network with 20 states (or
equivalently 20 integrator blocks) can be
approximated well using only 20 delay blocks. In
addition, an 80th order control system
requiring at least 30 integrators for a
satisfactory approximation can be
implemented using 2 integrators and 9 delay
blocks.
Project 2:
DelayBased Controller Design for
Hybrid Systems
In
engineered control systems, a common source of
delays is the discrete delay in clocked systems.
Computer controlled systems have been widely
used in a broad range of applications from
robotics, autopilot and radar to antilock
braking systems. Current silicon technology has
enabled the design of embedded systems operating
at very high frequencies. However, the
conventional methods for the synthesis of
sampleddata control systems require high
processing power to cope with numerical issues
if the sampling rate is relatively fast. More
precisely, increasing the sampling frequency
makes the digital controller extremely sensitive
to measurement noise and computational roundoff
errors. The situation becomes worse if the
sampling is subject to jitter and
irregularities.
Using
our results in Project 1, we proposed a robust
digitalcontrol scheme for continuoustime
systems that can be used in two important
scenarios: (i) having a high sampling frequency
with limited computational power (ii) having a
slow processor with jitter and irregular
sampling times. We showed that every
continuoustime stabilizing (LTI) controller can
be implemented in a hybrid form consisting of a
sampler, a digital processor, some socalled
``modified secondorder holds" and possibly a
unity feedback from the hold circuit to the
sampler. This hybrid controller benefits from
the fact that the increase of the sampling
frequency has a direct influence only on the
memory size of the controller, as opposed to its
parameters. This property makes the parameters
of the controller robust to the sampling rate
and irregularities.
(back to the top)
Consensus:
During the past few
decades, there has been a particular interest in
the area of distributed computation. The
distributed averaging problem, as a particular
case, is concerned with computing the average of
numbers owned by the agents of a group. This
problem has been investigated through the notion
of consensus in several papers, motivated by
different applications such as loadbalancing,
synchronization of coupled oscillators,
multiagent coordination and flocking, and state
estimation in wireless sensor networks.
Consider the distributed
average consensus problem in which the values
associated with a set of agents are to be
averaged in a distributed fashion. Since in many
applications all agents cannot update their
numbers synchronously, gossip algorithms have
been widely exploited by researchers to handle
the averaging problem asynchronously. On the
other hand, in light of communication
constraints, the data being exchanged between a
pair of agents is normally quantized. This has
given rise to the emergence of quantized gossip
algorithms.
Project 1:
Quantized Consensus by Means of Stochastic
Gossip Algorithm
In this work, we considered
a digitalcommunicationbased consensus problem,
where the initial values of the agents are real
numbers (as opposed to integers) whilst
only quantized data can be exchanged among the
agents. A weighted connected graph was
considered, where the weight of each edge
represented the probability of establishing a
communication between its corresponding vertices
through the updating procedure. First, we showed
that a quantized consensus is reached under the
stochastic gossip algorithm proposed in a recent
paper, for a wide range of updating parameters
and any arbitrary quantizer. We then studied the
convergence time of the gossip algorithm.
Project 2:
Quantized Consensus by Means of
Adaptive Stochastic Gossip Algorithm
We
showed in our Project 1 that the quantized
consensus is reached under a simple updating
protocol that deploys a fixed tuning factor. In
this work, we considered the case when the
tuning factor is allowed to be timedependent in
order to achieve two goals. First, this makes it
possible to study the numerical stability of the
protocol with a fixed tuning factor under a
small perturbation of this parameter.
Furthermore, exploiting a timevarying tuning
factor facilitates the implementation of the
consensus protocol and pushes the steady state
of the system towards an equilibrium point, as
opposed to making it oscillatory. Letting the
stochastic gossip algorithm proposed in Project
1 be timevarying is challenging due to
converting the underlying finitedimensional
problem to an infinitedimensional one for which
many results in Markov chain theory fail to
hold. (back
to the top)
Old Projects
(accomplished before 2008):
Before 2008, I worked on
several control related problems, some of which
are listed below:
Design of optimal
decentralized/distributed controllers for
interconnected systems.
Optimal cooperative control
of unmanned aerial vehicles
Different stability related
problems for distributed control systems
Robust stability and
stabilizability of polynomially uncertain
systems
Different problems arising in sampleddata
control systems
(back to the top)

