Access Type
Open Access Dissertation
Date of Award
January 2020
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
George Yin
Abstract
This dissertation focuses on a class of SA algorithms with applications to networked systems and is based on the published works that have been done jointly during my Ph.D. training. The networked systems are fundamentally characterized by interaction among control, communications, and computing, with applications in a vast array of emerging technologies such as smart grids, intelligent transportation systems, social networks, smart city, to name just a few. Networked systems encounter many environment uncertainties that are inherently stochastic. Besides the aforementioned advantages, the framework of SA can also accommodate multiple random processes and diversified system dynamics, even random and distributed delays, it therefore has been emerged as a promising platform to study advanced networked systems and has drawn increasing attention lately.
The first part addresses the problem of communication erasure channels on control performance of connected and automated vehicles under the weighted and constrained consensus framework. Random features of wireless communications introduce new types of uncertainties into networked systems and impact control performance significantly. Due to typical packet loss, erasure channels create random link interruption and switching in network topologies. This chapter models such switching network topologies by Markov chains and derives their probability transition matrices from stochastic characterizations of the channels. Impact of communication erasure channels on vehicle platoon formation and robustness under a weighted and constrained consensus framework is analyzed. By comparing convergence properties of networked control algorithms under different communication channel features, we characterize some intrinsic relationships between packet delivery ratio and convergence rate. Simulation case studies are performed to verify the theoretical findings.
The second part studies general stochastic approximation algorithms with switching which include many applications that had appeared on literature as special cases. We investigate the inherent interaction between control and communication systems by considering classes SA algorithms that accommodate random network topology, nonlinear dynamics, with complex system noise structures (additive or non additive), and other uncertainties in a unified framework. Interaction among control strategy and the multiple stochastic processes introduces critical challenges in such problems. By modeling the random switching as a discrete time Markov chain and studying multiple stochastic uncertainties in a unified framework, it is shown that under broad conditions, the algorithms are convergent. The performance of the algorithms is further analyzed by establishing their rate of convergence and asymptotic characterizations. Simulation case studies are conducted to evaluate the performance of the procedures in various aspects.
Recommended Citation
Nguyen, Thu Thi Le, "Stochastic Approximation And Applications To Networked Systems" (2020). Wayne State University Dissertations. 2442.
https://digitalcommons.wayne.edu/oa_dissertations/2442