AFOSR 2009–2014 Mehta & Meyn

**Project Summary **Complex networks can be found throughout engineering applications as well as the social, defense, biological and economic sciences. The Internet and the emerging wireless networks are forerunners of cyber-physical systems, such as network-driven sensor fusion for security applications, automation in highways and air-traffic control, control of objects at remote locations, and integrated building systems for energy and security requirements. As a result, “network science” is rapidly evolving discipline of vital societal importance.

This proposal is concerned with the science of inference and decision support in complex, interconnected systems. The focus of the proposed research is the development of mathematics and algorithms to address the following topics:

- Decision and control techniques in complex, networked systems.
- Robust inference techniques in multi-objective applications.
- Decomposition techniques that exploit inherent multi-scale dynamics.
- Fundamental limitations for inference and decision algorithms.

Research will build upon techniques introduced by the PIs on model reduction, robust hypothesis testing, systems and control theory, and machine learning.

Although these topics may appear only loosely connected, the mathematical foundations share strong common roots — Among the most compelling lie in Shannon’s view of model reduction, grounded in the information theoretic notion of entropy for stochastic processes. Our aim is to build bridges between dynamical systems and information theory to realize a unified framework for classification and model selection, performance analysis and distributed control design.

For topics in inference, it is now widely recognized that relative entropy provides an elegant foundation for algorithm construction and analysis. Information theory and entropy in its various forms are an important thread that runs throughout this proposal. A variety of system theoretic problems ranging from model reduction to fundamental limitations in control can be cast within the framework of information theory.

Apart from information theory, there are close parallels of the proposed work to the recent optimal prediction framework of A. Chorin that is itself related to the Mori-Zwanzig formalism for model reduction in physics. Other model reduction techniques will build on spectral theory for Markov models pioneered by Meyn, and the relaxation techniques described in the recent monograph.

These developments represent what we believe is an emerging paradigm of an *information theoretic basis *for complex systems. Our long-term goal is realize the vision of Norbert Wiener who famously said that* “Without this, mathematical systems theory remains limited to “simple problems” [?]”*. We will go a step further and claim that an information theoretic basis can provide an underpinning whereby complex nonlinear dynamics become an enabler (rather than a barrier) for control.

Portions of the foundations of this research were developed while the PIs were employed or visiting United Technologies Research Center (UTRC). On-going collaborations with UTRC will enrich the project through both scientific interactions and new applications.

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