CAREER: Information Theory of Dynamical Systems

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Modern technology aims for a massively and diversely connected world populated by a seamless network of intelligent, dynamically distributed systems engaged in a shared interaction with the physical world and each other through unreliable sensors, actuators, and noisy communication channels. Classical information theory, while it has long served as an enabler of high speed, long-distance communication for point-to-point, delay-tolerant communication systems using coding over long blocks of symbols, lacks ready solutions to the new challenges of the era of massive, dynamic connectivity. Evolving networks are rather delay sensitive, so coding over long blocks of observed data will not be feasible. Information exchanges frequently seek to maximizing payoff, rather than simply recover the information sent, and are often event-triggered, prompting new mathematical models and tools to gain insights into jointly optimal sensing/coding/control strategies for these systems. The project will also offer undergraduate research opportunities in conjunction with Caltech's Summer Undergraduate Research Fellowships (SURF) program, alongside outreach activities to middle and high school students via Caltech's Center for Teaching, Learning and Outreach, in order to encourage future scientists and engineers.The proposed research will advance the state of the art in understanding the fundamental trade-offs between communication and performance in dynamical systems. The project will draw upon the tools from both information theory and control theory to achieve its objectives, which are (1) to establish the fundamental information-theoretic trade-offs in delay-constrained causal source coding for dynamical systems under a distortion constraint; (2) to elucidate the information-theoretic trade-offs of control over noisy channels and propose new coding schemes with theoretical performance guarantees; and (3) to gain insight into jointly optimal sampling and coding strategies for tracking and control.