My research orientation lies at the intersection of dynamical systems and Control Theory, Optimization, and Graph Theory.These disciplines have recently emerged to define a new class of systems known as networked dynamic systems. While the application domains of this growing research area are vast, I believe them to be of particular interest for problems related to energy systems and multi-agent system. In particular, I have worked on projects dealing with relative sensing networks for deep space exploration, formation control of unmanned robots, and energy management systems for smart-grid applications.
Networked Dynamic Systems
NDS is at the intersection of three broad subjects
The general class of problems described by my research area are rich and diverse. At the heart of these problems are large-scale systems comprised of a group of coupled dynamic units, such as power generation sources in a power distribution network or a team of autonomous and unmanned vehicles. These systems interact via an exchange of information over a communication and sensing network. The complexity of this general class of problems arises from the heterogeneous dynamics of the systems comprising it, the diversity of interaction and communication mediums, and their scale in terms of the number of interacting systems and system interconnections. While research in this area is very active within the controls community, there remain many challenging and open problems that must be addressed before considering this a complete theory. The fundamental research questions I am looking at are
- How does the underlying connection topology of networked dynamic systems
affect its systems-theoretic properties?
- Can the connection topology be designed in conjunction with other synthesis
techniques and tools used for dynamic systems?
Canonical Models for NDS
A Canonical NDS Model
Identifying the structure of canonical models for NDS allows for a systematic way to study the properties of the system for both analysis and synthesis purposes. At times it is very straightforward to embed the connection topology of a networked system inside the overall dynamics. However, it becomes more enlightening to specify the connection topology as an additional parameter to the system dynamics, allowing for a more transparent understanding of how that parameter affects the system’s behavior. In this direction, I have defined 4 canonical models for NDS that describes how the connection topology couples each agent in the system
- NDS coupled at the output
- NDS coupled at the input
- NDS coupled at the state
- NDS coupled at the combination of input, output and state
Many of the well studied NDS models, such as the consensus protocol or applications using relative sensing, fit into this classification. In addition to this classification, I also introduce the notion of homogeneous and heterogeneous NDS to make explicit the impact of varying the dynamics of each agent in the ensemble. This has, in turn, led to interesting results relating traditional systems theoretic concepts with graph theoretic properties.
Optimization for Analysis and Design
Energy management for a solar-powered home.
Distributed optimization has become a vital aspect of research for multi-agent systems. On the one hand, it is important to study and develop algorithms that solve global optimization problem at a local and distributed level. This has immediate applications in problems related to the development of ``smart-grid'' power systems, as well as problems related to team decision-making. On the other hand, tools from optimization can lead to deep insights into the behavior of highly complex and non-linear dynamical system. One research thread is using tools from saddle-point optimization to study and explain the manifestation of synchronization or clustering in multi-agent systems.
Synchronization is a requirement for power systems, but can break and lead to clustering behavior if line capacities are limited (IEEE 30-bus system).