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Finite-dimensional controllers for robust regulation of boundary control systems

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  • We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the abstract setting and present finite-dimensional reduced order controllers. The controller design is then used for particular PDE models: high-dimensional parabolic equations and beam equations with Kelvin-Voigt damping. Numerical examples will be presented using Finite Element Method.

    Mathematics Subject Classification: Primary: 93C05, 93B52, 93D09; Secondary: 35K10.


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  • Figure 1.  Boundary controls located on red segments and regions of observations (blue)

    Figure 2.  Two extensions of boundary actuators

    Figure 3.  Output tracking of the boundary control of the 2D parabolic equation

    Figure 4.  Hankel singular values

    Figure 5.  Solutions of ODEs

    Figure 6.  Output tracking of the boundary controlled beam equation with two different extensions

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