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Optimization and control theory deal with different aspects of the following problem: given that certain parameters or inputs for a static or dynamic system are available for design, how should they be selected such that the resulting "closed loop" or optimized system has the desired properties? The mathematics of such an intuitive problem that seems to be at the heart of all engineering sciences, rather surprising, span a lot of distinct mathematical disciplines, from real, complex, functional analysis, to differential and algebraic topology, to graph theory and combinatorics, and of course, to optimization.
In our group, our research has traditionally spanned the area of semidefinite programming and its extensions to problems in feedback design and estimation. More recently, we have considered the area of online optimization in distributed decision-making over networks, as well as the application of optimization and feedback control to energy efficient aerospace systems- the so-called "mini-grid" on aerospace vehicles. Energy efficient flight can also be achieved by taking advantage of solar energy- in this context, we have looked at optimizing the vehicle's trajectory that best utilizes the available solar energy.
Funding acknowledgements: NSF, ONR, Boeing
Some of our ongoing projects include: