On control design for PDEs with space-dependent diffusivity or time-dependent reactivity

Authors:
Andrey Smyshlyaev;Miroslav Krstic
Affiliations:
Department of Mechanical and Aerospace Engineering, University of California at San Diego, 9500 Gilman Drive, LaJolla, CA 92093-0411, USA;Department of Mechanical and Aerospace Engineering, University of California at San Diego, 9500 Gilman Drive, LaJolla, CA 92093-0411, USA
Venue:
Automatica (Journal of IFAC)
Year:
2005

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Abstract

In this paper the recently introduced backstepping method for boundary control of linear partial differential equations (PDEs) is extended to plants with non-constant diffusivity/thermal conductivity and time-varying coefficients. The boundary stabilization problem is converted to a problem of solving a specific Klein-Gordon-type linear hyperbolic PDE. This PDE is then solved for a family of system parameters resulting in closed-form boundary controllers. The results of a numerical simulation are presented for the case when an explicit solution is not available.