Adaptive State Feedback Control of Lorenz Systems to Its Non-Trivial Equilibrium

<p>The complex Lorenz system is a simplified nonlinear dynamical system, which is derived from the Navier-Stokes equations that govern a closed thermal convection loop. The Lorenz system is chaotic for large Rayleigh number. In this chaotic regime, we implement a linear state feedback controller to stabilize the state trajectory at its original nontrivial equilibrium. The state variable for feedback is easily measurable. The system is proved to be globally asymptotically stable with a optimal feedback gain. The stability bound is improved over the previous result. We also established globally stability of the adaptively control system, where the system parameters are unknown. We present numerical simulations to demonstrate the stability, transient and steady state responses, and the performance of the state feedback controller.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2014

Author dc:creator

• Tran, Anh V

Contributors dc:contributor

• Yan Wu
• Alex Stokolos
• Frank Goforth

• ETD
• adaptive control
• Lyapunov stability
• feedback control
• multi-equilibrium
• natural convection loops
• Lorenz system
• Control Theory

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1109

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2116