Term of Award

Spring 2023

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Yan Wu

Committee Member 1

John Shijun Zheng

Committee Member 2

Yongki Lee

Abstract

In this work, we obtain a system of nonlinear differential equations from a series of laterally coupled quad-loop systems, which is modeled by a system of Navier-Stokes equations. The system exhibits chaotic and hyperchaotic phenomena when the driving parameters pass the threshold value. The main objective of this research is to stabilize the flows well into their chaotic regime via a minimum number of state feedback controllers. The work models and simulates a coupled thermosyphon system with different initial conditions to determine the optimal gains needed to achieve stability. Explicit bounds on the feedback gains are derived based on the Lyapunov stability theory. The bounds on the feedback gains interact with each other and system parameters play a crucial role in driving the state trajectories. Numerical simulations further demonstrate the effectiveness of the proposed control system configuration.

OCLC Number

1402278766

Research Data and Supplementary Material

No

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