A Two-Time-Scale Approach
Focusing on singular perturbation methods, this book systematically addresses systems relevant to queuing theory, control and optimization, and manufacturing. It consolidates concepts that were previously dispersed across various sources, making it a comprehensive reference for understanding these interconnected areas.
Focusing on stochastic approximation algorithms, this book delves into their theoretical and applied aspects, stemming from foundational work by Robbins, Monro, Kiefer, and Wolfowitz in the 1950s. It explores the dynamics of stochastic processes through recursive adjustments of parameters based on noise-corrupted observations. The text emphasizes qualitative and asymptotic properties of these algorithms, including their continuous time counterparts, and discusses their application in root-finding problems where functions are not explicitly known.
Focusing on two-time-scale Markov chains in discrete time, this book explores their applications in optimization and control across various fields, including manufacturing and finance. It emphasizes designing system models that account for uncertainty in complex systems influenced by jump or switching processes. A key feature is the use of multi-time scales, which allows for reducing complexity through decomposition. The text also addresses challenges in treating nearly decomposable systems and employs singular perturbation methods to analyze these dynamics effectively.
This book provides a comprehensive exploration of quantized information in system identification, targeting graduate students and professionals. It discusses methodologies for systems with quantized outputs, addressing both linear and nonlinear systems, various noise types, and offering insights into control capabilities with limited sensor data.