Null controllability of the heat equation using flatness

2013/10/23 by Philippe Martin, Martin, Philippe, Lionel Rosier +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1310.6179

openalex publication_date 2013/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive in a direct and rather straightforward way the null controllability of the N-dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This yields an explicit control law achieving the exact steering to zero. Replacing the involved series by partial sums we obtain a simple numerical scheme for which we give explicit error bounds. Numerical experiments demonstrate the relevance of the approach.

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