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Degrees & Accolades:

Engineering & Applied Science (First Year Instructor Teaching Award, 2014 & 2016)

Postdoc (University of Illinois, Urbana-Champaign, 2012-13)
Postdoc (University of California, San Diego, 2009-12)
Ph.D. (÷ÈÓ°Ö±²¥, 2009)
M.Sc. (Shiraz University, 2005)
B.Sc. (Shiraz University, 2002)

Research Profile:

My general research interests lie within the areas of systems and controls and its intersections with a variety of subjects in mathematics. My recent research is focused on distributed control and optimization, where the control input is generated in a decentralized manner, by a group of individuals each with limited information about the state of the system. I also work on nonlinear stabilization and geometric control theory, and have a broad interest in Riemannian geometry and geometric mechanics. My research has intersections with network sciences and graph theory, stochastic processes, algorithm design, machine learning, social and economic networks, and game theory.

Research Areas:

Intersections of non-convex optimization, machine learning, and control theory: Stochastic gradient methods are at the heart of recent advances in optimization and machine learning. Besides neural networks, these include policy gradient methods, temporal difference learning, and actor-critic dynamics in reinforcement learning. These advancements have had profound impacts on model-free control, where decisions are made based on data. The theoretical problems in this area combine ideas from stochastic analysis, dynamical systems, and geometric methods.

Universal approximation theory in machine learning: Neural networks possess inherent universal approximation power, which means they can effectively approximate functions given enough nodes and layers. Universal approximation is a classical topic; however, we have only recently been able to theoretically characterize it for settings with bounded width. Techniques from control theory, particularly geometric and optimal control, have been shown to be key, with much still to discover for modern architectures and networks not studied in isolation. There is also an interesting intersection of this topic with optimal transport theory.

Structural frameworks for control of ensemble systems: In many real-world scenarios, some system parameters are only probabilistically known. Classical control notions, such as controllability and stabilizability, often rely on the deterministic knowledge of these parameters. Ensemble control theory provides the foundation for studying such systems, with fascinating intersections with optimal transport theory, identification theory, model-free control, and partial differential equations. Research in this area intersects with functional analysis, graph theory, differential geometry, and Lie theory.