Doctor of Philosophy
D. Gary . Harlow
In the initial part of the dissertation, we study a time-delay first-order dynamical network. We characterize its performance in terms of the spectrum of the Laplacian matrix of the graph. Later in Section 2.3 we study properties of this performance function. We show that it is increasing with respect to time-delay, and it is convex with respect to weight of the edges of the coupling graph. In section 2.4, we discuss topologies with optimal performance. Furthermore, we quantify a sharp lower bound on the best achievable performance for a first-order network with a fixed time-delay.
In presence of time-delay, the H2-norm performance of a first-order consensus network is not monotone decreasing with respect to connectivity, which makes challenges in design of the optimal network since increasing connectivity may actually deteriorate the performance. Then, we present methods to improve the performance measure.
We categorize these procedures as growing, reweighting, and sparsification and is discussed in the rest of Chapter 2.
The second part of the dissertation is devoted to centrality of components in a network with respect to time-delay and coupling graph in presence of different sources
of noise where we study the of nodes in the presence of four types of uncertainty, namely dynamics noise, sensor noise, receiver noise, and emitter noise. Influence of the links is studied in later, in which we address the importance of the links in the presence of relative measurement noise and communication noise. We address order of precedence of components of the network in and lastly, we provide several examples to show the effect of connectivity and time-delay on the order of precedence.
In the third part, we address a class of second-order dynamical network that is used for modeling a platoon of cars. First, we characterize the performance measure in terms of time-delay, spectrum of the Laplacian matrix, and other system parameters. Then, we discuss the optimal topology and the fundamental limit on the best achievable performance for a second-order platoon. Then we discuss and efficient method for designing the optimal platoon in the presence of time-delay.
Lastly, we study another class of second-order dynamical network which is deployed for modeling network of synchronous generators. First, we address the stability of the network in the presence of time-delay. Then, similar to previous chapters, we characterize the performance measure in terms of time-delay, spectrum of the Laplacian matrix, and other system parameters. Then we discuss and efficient method for designing the optimal distributed controller in the presence of time-delay.
Ghaedsharaf, Yaser, "Performance Analysis and Design of Consensus Dynamics in the Presence of Time-delay" (2020). Theses and Dissertations. 5658.
Available for download on Friday, January 29, 2021