Numerical discretization of boundary control problems for systems of balance laws: feedback stabilization

DOI10.1016/j.ejcon.2017.02.002zbMath1367.49022OpenAlexW2591062512WikidataQ60471914 ScholiaQ60471914MaRDI QIDQ2011965

Peter Schillen, Simone Goettlich

Publication date: 27 July 2017

Published in: European Journal of Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejcon.2017.02.002

zbMATH Keywords

Lyapunov functionfeedback stabilizationsystems of balance laws

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Hyperbolic conservation laws (35L65) Discrete approximations in optimal control (49M25) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (7)

Numerical feedback stabilization with applications to networks ⋮ Numerical boundary control for semilinear hyperbolic systems ⋮ Feedback stabilization for a coupled PDE-ODE production system ⋮ Numerical boundary feedback stabilisation of non-uniform hyperbolic systems of balance laws ⋮ An algebraic condition for the exponential stability of an upwind difference scheme for hyperbolic systems ⋮ Input-to-state stability of non-uniform linear hyperbolic systems of balance laws via boundary feedback control ⋮ Discretized feedback control for systems of linearized hyperbolic balance laws

Cites Work

• Unnamed Item
• Stability and boundary stabilization of 1-D hyperbolic systems
• Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws
• Gas flow in pipeline networks
• Lyapunov stability analysis of networks of scalar conservation laws
• Robust boundary control of systems of conservation laws
• Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions
• Exact controllability for first order quasilinear hyperbolic systems with vertical characteristics
• The effect of boundary damping for the quasilinear wave equation
• Boundary feedback control in networks of open channels.
• A study of numerical methods for hyperbolic conservation laws with stiff source terms
• Global boundary controllability of the de St. Venant equations between steady states
• Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws
• On Lyapunov stability of linearised Saint-Venant equations for a sloping channel
• Boundary control with integral action for hyperbolic systems of conservation laws: stability and experiments
• Boundary feedback stabilization of the telegraph equation: decay rates for vanishing damping term
• Electric transmission lines: Control and numerical discretization
• Existence of classical solutions and feedback stabilization for the flow in gas networks
• Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems
• Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems
• Finite Volume Methods for Hyperbolic Problems
• Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm
• A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws
• Boundary Controllability of Nonlinear Hyperbolic Systems

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