Adaptive Control of a Linear Hyperbolic PDE with Uncertain Transport Speed and a Spatially Varying Coefficient
Peer reviewed, Journal article
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Date
2020Metadata
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Original version
Mediterranean Conference on Control and Automation (MED). 2020, 945-951. 10.1109/MED48518.2020.9183027Abstract
Recently, the first result on backstepping-based adaptive control of a 1-D linear hyperbolic partial differential equation (PDE) with an uncertain transport speed was presented. The system also had an uncertain, constant in-domain coefficient, and the derived controller achieved convergence to zero in the L ∞ -sense in finite time. In this paper, we extend that result to systems with a spatially varying in-domain coefficient, achieving asymptotic convergence to zero in the L ∞ -sense. Additionally, for the case of having a constant in-domain coefficient, the new method is shown to have a slightly improved finite-time convergence time. The theory is illustrated in simulations.