# Research

This is very out of date. Sorry. Will try to fix it. Stay tuned.

"Professor Doyle's current **research** interests are in theoretical foundations for complex networks, primarily in network engineering and biology." He is also "interested in multiscale physics and financial markets, and the interplay between robustness, feedback, control, dynamical systems, computation, communications, and statistical physics." <http://www.cds.caltech.edu/people/> Aug 2008

Prof. Doyle has "applied complex ideas of robust design and control to many fields and is working on a unified theory of control in engineering, physics and biology." <http://www.ieee.org/portal/pages/about/awards/bios/2004controlsystems.html> Aug 2008

## Contents

## Current Projects

- Systems Biology (Fiona Chandra, Genti Buzi)
- Fundamental constraints and trade-offs of autocatalytic networks.
- Collaborators: Hana El-Samad, Antonis Papachristodoulou

- Fluids: Turbulence Modeling (Dennice Gayme)
- Collaborators: Bassam Bamieh, Beverly McKeon

- Physiology: Dynamic Modeling of Heart Rate Variability (Li Na, Jerry Cruz)
- Heart rate (HR) in healthy humans has high variability, and loss of this HR variability (HRV) is a signature of stress, fatigue, aging, or disease1-9. Correlating health and high HRV using time series analyses is popular in clinical and athletic training10 research, but its practical impact has been limited by lack of specific physiological mechanisms explaining HRV patterns. Conjectures attributing the cryptic etiology of HRV to complex feedbacks and nonlinear dynamics have similarly lacked mechanistic explanation. We leverage concepts from physiology, evolution, and control theory to analyze data from exercising athletes and develop mechanistic models explaining correlations between health, stress, and HRV.

- Internet and Networking (Lijun Chen, Javad Lavaei, Somayeh Sojoudi)
- Collaborators: Steven Low

- Economics (Jerry Cruz)
- Market Bubbles and Crashes: We use tools from mathematical finance and stochastic control theory to investigate asset price bubbles and crashes in financial markets. We wish to gain insight using models that account for financial intermediation and associated frictions. Moreover, recent local-martingale characterizations of bubbles may provide avenues into developing new methods of empirical testing for bubbles.

- Distributed Control (Javad Lavaei, Nader Motee, Li Na)
- Designing Games for Distributed Opitmization (Li Na)

The central goal in multiagent systems is to design local control laws for the individual agents to ensure that the emergent global behavior is desirable with respect to a given system level objective. Ideally, a system designer seeks to satisfy this goal while conditioning each agent's control law on the least amount of information possible. Unfortunately, there are no existing methodologies for addressing this design challenge. The goal of this research is to address this challenge using the field of game theory. We develop a systematic methodology for distributed optimization using the framework of state based potential games.

- Designing Games for Distributed Opitmization (Li Na)

## Research Grants

- NSF award: ITR COLLAB: Theory and Software Infrastructure for a Scalable Systems Biology, 2003-present

- Some joint projects with Prof. Richard Murray (with links to his wiki below)
- Specification, Design and Verification of Distributed Embedded Systems (MURI/AFOSR)
- Networked Feedback Systems in Biology (ARO ICB)
- Model-Based Design and Qualification of Complex Systems (Boeing)

- Some joint grants with Prof. Steven Low:
- MURI Analysis and modeling of networks with long range dependence (LRD) characteristics (PI - Jean Walrand, UC Berkeley; Co-PIs - John Doyle, Steven Low, R. Srikanth (UIUC), V. Anantharam & A. Zakhor (UC Berkeley), D. Towsley & W. Gong (U. Mass. Amherst)2008
- NSF RI WAN in Lab (Newman, Psaltis, Yip) 2003-08
- NSF NeTS Collaborative Research: Optimization and Games in Interdomain Routing 2006
- NSF STI Multi-Gbps TCP: Data Intensive Networks for Science & Engineering (Bunn, Newman) 2002-05
- NSF ITR Optimal and Robust TCP Congestion Control 2001-04
- ARO DURIP Hybrid WAN in Lab (Newman, Psaltis, Yip) 2004-05
- ARO Network Research Analytical Theory of Protocols 2002-05
- ARO Network Science Networked control systems (Murray, Parrilo (MIT)) 2005-2006

(Note that other Co-PI are noted in brackets on these joint grants with Prof. Low and Prof. Doyle)

## Past Projects

Caltech

- HOT : Highly Optimized/Organized Tradeoffs/Tolerance, A unified theory of complex networks
- SOSTOOLS : Software for analysis of complex systems
- "Mathematical Infrastructure for Robust Virtual Engineering" MURI award 1996
- Past projects with Prof Murray (links to his wiki)

Other

## Collaborative groups

- CIMMS: Center for Integrative Multiscale Modeling and Simulation
- Prof. Richard Murray
- Prof. Hana El-Samad (UCSF)
- Lee Center for Networking
- Netlab

- and more...

## See also

### More research links

Caltech

UCSB