The project seeks to develop a comprehensive framework for obtaining data driven models for a class of nonlinear systems that arise in the context of a broad range of applications that entail extracting information from high volume data streams. Obtaining these models is the first step towards developing a new class of systems with substantially enhanced capabilities to extract information sparsely encoded in multimodal, extremely large data sets. In particular, as a proof of concept, this project will focus on sustainable water quality management in urban environments, a problem that affects over one billion people in the Developing World and leads to losses estimated at over $2 billion/year in the US alone. From an education standpoint, this theme will be used to link a full range of distinct undergraduate and graduate courses, from systems theory, environmental and hydrologic engineering to machine learning, with emphasis on robustness and computational complexity. Undergraduate students will be engaged in research through the OUR Charles (Opportunities for Undergraduate Research on the Charles River) program.
While control of switched systems has made considerably progress in the past few years, the problem of identifying and validating hybrid models amenable to be used by these methods is far from solved. The present proposal aims at closing this gap by developing a computationally tractable framework for robust identification and model (in)validation of switched Hammerstein/Wiener systems. Its conceptual backbone is a combination of systems theory, semi-algebraic geometry and convex optimization elements that emphasizes robustness and computational complexity issues. The main idea is to recast the identification and model (in)validation of switched systems into a sparse semi-algebraic optimization form and to exploit recent advances in convex optimization to develop scalable, computationally tractable methods to solve these problems.
The advantages of the proposed approach include the ability to: (a) Address problems beyond the capabilities of existing techniques due to a combination of a lack of a comprehensive theoretical framework and poor scaling properties. (b) Directly accommodate and respect features that are key to success in the relevant application domains, such as sparse interconnection structures. (c) Exploit a hitherto largely unexplored connection between systems identification and the problem of extracting actionable information from very large data sets.