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Research Summaries
Click on each of the figures below for detailed descriptions and references
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Network topology of coordinated/cooperative control problems imposes certain fundamental limit-of-performance bounds. This is one promising approach to the question of network controllability. We investigate large networks with some structure (e.g. lattices, tori, fractal graphs). Amongst other things, this approach also yields interesting implications on fundamental limitations for vehicular platoons control.
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Probably the most important question in distributed control design is about controller architecture, e.g. which sensors should communicate with which actuators? how much degradation in performance is incurred when imposing additional link constraints, etc. In general, these questions are notoriously difficult (e.g. decentralized control). However, there are important classes of problems where surprising answers are obtained.
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Consensus with random link failures is a prototype problem for studying the dynamics of stochastic networks. In its simplest form, this problem can be recast as linear systems with multiplicative noise, or equivalently as uncertain systems with structured stochastic uncertainty. Such systems can exhibit complex phenomena such as heavy tailed distributions and Levy flights, yet are more tractable than completely general stochastic systems.
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Turbulence and transition in streamlined bodies such as pipes, flat plates and boundary layers is still considered one of the most difficult and incompletely understood scientific problems. In the past two decades, a new approach has emerged to this problem which has inspired our work, in which transition is not merely a stability (linear or nonlinear) problem, but rather a question of robustness and fragility. This new mathematical approach has fascinating connections with the subject of Robust Control.
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Optimal control problems arise in laser chemistry for controlling molecular bond vibrational states using envelop shaping of femtosecond laser pulses. Even for the simplest of molecules, the design problem is computationally prohibitive. It turns out that there is a natural time-scale separation in the optimal control problem, which yields an optimal timed schedule of intermediate energy level transitions. The resulting scheduling problem is much less stiff and computationally tractable.
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Thermoacoustic phenomena occur whenever there is significant coupling between acoustic and convective-heat-transfer dynamics. Thermoacoustic instabilities occur in certain combusters, Ramjets and Scramjets, and solid-fuel rocket engines. In such devices, thermoacoustic phenomena are undesirable and sabotage proper operation. On the other hand, there are fascinating heat engines and pumps that operate based on thermoacoustic effects. These novel energy conversion devices have almost no moving parts. It is internal, high power density acoustic waves that do the mechanical work, replacing the transitional pistons, cranks and turbines.
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TBD
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Older Projects
This is older work which I am happy to answer questions about, although I am not actively working in those areas at present
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