Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems

By Jean-Michel Coron, G. Bastin, Brigitte d'Andréa-Novel. SIAM Journal of Control and Optimization, 2008

305 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/96cf58b7b98197138b82716ae42cb91320650aa1

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In Applied Mathematics

In Control and Systems Engineering

In Mechanics of Materials

Citations in the corpus

Control of the Continuity Equation with a Non Local Flow (2009, background): “d to ρo. We emphasize that all this is obtained within the framework of non smooth solutions, diﬀerently from many results in the current literature that are devoted to diﬀerentiability [21], control [18, 19] or optimal control [15] for conservation laws, but limited to smooth solutions. Furthermore”
Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input (2013, background): “In [11] and [38] control laws for a system of two coupled nonlinear PDEs are derived, whereas in [7], [10], [21], [30], [31] sufficient conditions for exponential stability are given for various classes of quasilinear first-order hyperbolic systems.”
Local rapid stabilization for a Korteweg–de Vries equation with a Neumann boundary control on the right (2013, methodology): “This method can be used to get rapid stabilization for some partial differential equations (see, for example, [8]).”
Strict Lyapunov functions for semilinear parabolic partial differential equations (2011, methodology): “More precisely, based on [4], strictification techniques have been used for a class of time-varying hyperbolic equations in [24].”
Boundary exponential stabilization of 1-D inhomogeneous quasilinear hyperbolic systems (2015, background): “to design dissipative boundary conditions for nonlinear homogeneous hyperbolic systems in the context of both C(1) and H(2) norm [4, 5, 6].”
Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs (2015, methodology): “Later, the so-called Control Lyapunov Functions methods emerged, enabling the design of dissipative boundary conditions for nonlinear hyperbolic systems in the context of both C1 norm and H2 norm [5], [6], [9].”
Using hyperbolic systems of balance laws for modeling, control and stability analysis of physical networks (2009, background): “The proof of this theorem is much more complicated than its linear counterpart and can be established by using the approach followed in [6].”
Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system (2011, methodology): “More recently, an approach using control Lyapunov functions has been developed, for 2× 2 quasilinear systems [2] and n × n quasilinear systems [3].”