CAREER: Information Theory of Dynamical Systems

现代技术的目标是建立一个大规模和快速连接的世界，由智能的无缝网络组成，动态分布式系统通过不可靠的传感器，执行器和嘈杂的通信信道与物理世界和彼此进行共享交互。经典的信息理论，虽然它长期以来一直作为一个使能器的高速，长距离通信的点对点，延迟容忍的通信系统使用编码长块的符号，缺乏现成的解决方案，大规模的时代的新挑战，动态连接。演化网络对延迟相当敏感，因此在长的观测数据块上进行编码将是不可行的。信息交换经常寻求最大化回报，而不是简单地恢复发送的信息，并且通常是事件触发的，促使新的数学模型和工具来深入了解这些系统的联合最佳传感/编码/控制策略。该项目还将与加州理工学院的夏季本科生研究奖学金（SURF）计划一起提供本科生研究机会，并通过加州理工学院的教学，学习和推广中心为初中和高中学生开展推广活动，为了鼓励未来的科学家和工程师。拟议的研究将推进了解基本贸易的最新技术水平-在动态系统中沟通和性能之间的平衡。本计画将利用资讯论与控制论的工具来达成其目标：（1）建立失真限制下动态系统延迟限制因果来源编码的基本资讯论权衡;（2）阐明控制杂讯通道的资讯论权衡，并提出具有理论效能保证的新编码方案;以及（3）深入了解用于跟踪和控制的联合最优采样和编码策略。

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.