Singular optimal control: A linear 1-D parabolic–hyperbolic example

By Jean-Michel Coron, Sergio Guerrero. Asymptotic Analysis, 2005

94 citations recorded by the source corpus.

We consider the problem of the null controllability of a family of 1-D linear control parabolic equations depending on two parameters, namely the viscosity and the coefficient of the transport term. We study the dependence, with respect to these parameters and the time of controllability, of the norm of the optimal controls. In particular we give estimates on the optimal control as the viscosity tends to 0.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/6d46be6e5728e0aa9f324ac393d4bb118153209f

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Carleman estimates for parabolic equations and applications (2009, background): “As very limited references on the basis of the Carleman estimate, we refer to the following papers: (1) Parabolic equations: [37, 55, 56, 63, 64, 127].”
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels (2020, background): “Such a convergence result would also give additional insights into questions related to control theory (see [4]), in the spirit of [22, 34, 29, 47].”
Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, background): “For instance, in [138] the Carleman inequalities play a key role when deriving the continuity of controls for the following singular perturbation problem connecting dissipative wave equations with the heat equation εutt −∆u+ ut = f1ω, and in [36] where the same issue is addressed for the convective ”
A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit (2010, background): “The problem under view was first introduced and studied by Coron and Guerrero [5].”