Kybernetika 61 no. 5, 666-687, 2025

Explicit control law for a heat equation based on output tracking

Cuihua He, Ke Wang and Zhongcheng ZhouDOI: 10.14736/kyb-2025-5-0666

Abstract:

Boundary control to track the output reference of the heat equation is considered. A control input is implemented at one boundary while requiring the other boundary to track the output reference. By introducing the error system and backstepping transformation, the control law is designed. The undetermined coefficient method and two identities are used to obtain the analytical solution of the kernel function by complex mathematical calculation. This establishes an explicit control law and ensures that the error system can effectively achieve the desired closed-loop stability. Simulation results validate the proposed theoretical results.

Keywords:

backstepping, boundary control, output tracking

Classification:

93C20, 35K05, 93D15, 93D23

paper.pdf

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