“Information-theoretic tradeoffs in control”
Dr. Victoria Kostina, Caltech
Wednesday, April 19, 2017 2:00 – 3:00PM EEB 248
Abstract: Consider a flying drone controlled from the ground by an observer who communicates with it via wireless. We are interested in how well the drone can be controlled via a channel that accepts r bits/sec. Formally, the controller of a linear stochastic system aims to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We characterize the optimal tradeoff between the communication rate r bits/sec and the limsup of the expected cost b. We consider an information-theoretic rate-cost function, which quantifies the minimum mutual information between the channel input and output, given the past, that is compatible with a target LQR cost. We provide a lower bound to the rate-cost function, which applies as long as the system noise has a probability density function, and which holds for a general class of codes that can take full advantage of the memory of the data observed so far and that are not constrained to have any particular structure. Perhaps surprisingly, the bound can be approached by a simple variable-length lattice quantization scheme, as long as the system noise satisfies a smoothness condition. The quantization scheme only quantizes the innovation, that is, the difference between the controller's belief about the current state and the encoder's state estimate.
Bio: Victoria Kostina joined Caltech as an Assistant Professor of Electrical Engineering in the fall of 2014. She holds a Bachelor's degree from Moscow institute of Physics and Technology (2004), where she was affiliated with the Institute for Information Transmission Problems of the Russian Academy of Sciences, a Master's degree from University of Ottawa (2006), and a PhD from Princeton University (2013). She joined Caltech as an Assistant Professor of Electrical Engineering in the fall of 2014. Her PhD dissertation on information-theoretic limits of lossy data compression received Princeton Electrical Engineering Best Dissertation award. She is also a recipient of Simons-Berkeley research fellowship (2015). Victoria Kostina's research spans information theory, coding, wireless communications and control.