Fast Signal Processing and Control Algorithms for Complex Hierarchical Systems

复杂的动力学行为是许多现实世界系统所固有的，包括电信网络、金融市场和生物系统。用于这种大规模复杂系统的高性能信号处理和控制算法通常在计算上非常昂贵。在许多应用中出现的一类重要的大规模马尔可夫模型显示出显着的层次性质，显示出强相互作用的某些集群的状态和弱相互作用之间的集群。通过利用这一特性，该项目将设计和分析具有严格性能保证的新型低复杂度信号处理和控制算法。此外，该项目将探索使这些算法分层的可能性，以便通过分散化易于实现。

Complex dynamical behaviour is inherent to many real-world systems including telecommunications networks, financial markets and biological systems. High performance signal processing and control algorithms for such large-scale, complex systems are computationally very expensive in general. An important class of large-scale Markovian models arising in many applications shows a remarkable hierarchical property, displaying strong interactions within certain clusters of states and weak interactions among these clusters. By utilizing this property, the proposed project will design and analyze novel reduced-complexity signal processing and control algorithms with rigorous performance guarantees. In addition, this project will explore possibilities of making these algorithms hierarchical such that they are easy to implement through decentralization.