Population systems are ubiquitous in nature and engineered infrastructures at different scales. Finely manipulation of collective behavior of such dynamic populations is an essential and compelling task in many emerging applications from neural stimulation and robot swarms to nuclear magnetic resonance spectroscopy and imaging. A bottleneck in studying such large-scale systems is that control and observation can only be implemented at the population level, through broadcasting a single input signal to all the systems in the population and through collecting aggregated system-level measurements of the population, respectively. These limitations give rise to challenging problems and new control paradigms involving underactuated manipulation of dynamic ensembles.
In this talk, I will present a moment-based approach to controllability analysis and control design for linear ensemble systems. This method maps an ensemble system to an associated moment system by a suitable choice of a moment transformation, which inherits a banded structure that enables control-theoretic analysis and facilitates control design. In addition, I will also discuss my recent progress on locating optimal pinning controls for complex oscillatory networks
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