Flatness-based boundary control of a class of quasilinear parabolic distributed parameter systems

2002/01/01 by A. F. Lynch, Alan F. Lynch, J. Rudolph +1 · 2 citations
Engineering · Computer Science · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics

paper · doi:10.1080/00207170210163640

Abstract

Motion planning and control of a boundary controlled quasilinear parabolic partial differential equation in one spatial variable is considered. The approach relies on a flatness property of the system; namely, that the system solution can be differentially parameterized in terms of a flat output which, in the case considered, is a boundary value. Such a parameterization allows straightforward motion planning and computation of a control law. The approach is based on power series in the spatial variable, and the convergence of these series is ensured by choosing the flat output to be a nonanalytic, smooth function of appropriate Gevrey class.

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• Tracking controllability on moving targets for parabolic equations
• A new approach to boundary control of semilinear parabolic PDEs that yields linear tracking error dynamics

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