We consider the boundary control problem to stabilize the power of a signal and a pump propagating down a Raman amplifier. This is essentially an initial-boundary value problem (IBVP) of a hyperbolic system with Lotka-Volterra type nonlinearities. We treat the system as a control problem with states in the function space and use Lyapunov-based analysis to demonstrate asymptotic stability in the C_0 and the L_2-sense. The stability conditions are derived for closed-loop systems with a proportional controller and a dynamic controller, and confirmed by simulations in MATLAB.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/24243 |
| Date | 06 April 2010 |
| Creators | Chang, Chia-wei Liz |
| Contributors | Pavel, Lacra |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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