Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary

DOI10.1016/j.sysconle.2009.04.005zbMath1166.93025OpenAlexW2137817450WikidataQ59621748 ScholiaQ59621748MaRDI QIDQ2390547

Andrey Smyshlyaev, Krstić, Miroslav

Publication date: 23 July 2009

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.sysconle.2009.04.005

zbMATH Keywords

boundary controlwave equationbacksteppingdistributed parameter systems

Mathematics Subject Classification ID

Related Items (47)

Output feedback stabilization for multi-dimensional Kirchhoff plate with general corrupted boundary observation ⋮ Sliding mode boundary control for vibration suppression in a pinned-pinned Euler–Bernoulli beam with disturbances ⋮ A novel observer-based approach for the exponential stabilization of the string PDE with cubic nonlinearities ⋮ Stabilization of higher order Schrödinger equations on a finite interval. II ⋮ Null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach ⋮ Adaptive observer design for wave PDEs with nonlinear dynamics and parameter uncertainty ⋮ Compensating PDE actuator and sensor dynamics using Sylvester equation ⋮ Boundary state feedback exponential stabilization for a one-dimensional wave equation with velocity recirculation ⋮ Adaptive rejection of harmonic disturbance anticollocated with control in 1D wave equation ⋮ Output tracking for a 1-D heat equation with non-collocated configurations ⋮ Boundary stabilization of a \(1\)-D wave equation with multi-point velocity recirculations ⋮ Output feedback stabilization of an unstable wave equation with observations subject to time delay ⋮ Observability and observer design for a class of hyperbolic PDEs with van de Pol type boundary conditions ⋮ ISS-based robustness to various neglected damping mechanisms for the 1-D wave PDE ⋮ Boundary stabilization of a cascade of ODE-wave systems subject to boundary control matched disturbance ⋮ Output tracking and disturbance rejection for 1-D anti-stable wave equation ⋮ Stabilization involving condition-based adaptive control of an uncertain wave equation for the vibration of a flexible string ⋮ The active disturbance rejection control approach to output feedback stabilization of an anti-stable wave equation with corrupted boundary observation ⋮ Output Feedback Stabilization of Coupled Reaction-Diffusion Processes with Constant Parameters ⋮ Boundary output feedback stabilization for a cascaded wave PDE-ODE system with velocity recirculation and matched disturbance ⋮ On the regularized solutions of optimal control problem in a hyperbolic system ⋮ Output-feedback stabilization of an anti-stable Schrödinger equation by boundary feedback with only displacement observation ⋮ The boundary control strategy for a fractional wave equation with external disturbances ⋮ Output-feedback adaptive control of a wave PDE with boundary anti-damping ⋮ Control of PDE-ODE cascades with Neumann interconnections ⋮ Optimal Time for the Controllability of Linear Hyperbolic Systems in One-Dimensional Space ⋮ Boundary control of coupled reaction-diffusion processes with constant parameters ⋮ Late-lumping backstepping control of partial differential equations ⋮ Stabilization of one-dimensional wave equation by non-collocated boundary feedback ⋮ Static boundary feedback stabilization of an anti-stable wave equation with both collocated and non-collocated measurements ⋮ Null-controllability of linear hyperbolic systems in one dimensional space ⋮ Optimal boundary displacement control at one end of a string with a medium exerting resistance at the other end ⋮ Dynamic feedback stabilization of an unstable wave equation ⋮ Active disturbance rejection control based on weighed-moving-average-state-observer ⋮ Arbitrary decay rate for two connected strings with joint anti-damping by boundary output feedback ⋮ Observer design and stability analysis for a class of PDE chaotic systems ⋮ Backstepping approach to the arbitrary decay rate for Euler–Bernoulli beam under boundary feedback ⋮ UDE-based robust boundary control for an unstable parabolic PDE with unknown input disturbance ⋮ Simultaneous identification of damping coefficient and initial value for PDEs from boundary measurement ⋮ Boundary control of partial differential equations using frequency domain optimization techniques ⋮ Stabilization of One-dimensional Wave Equation with Van Der Pol Type Boundary Condition ⋮ Lyapunov approach to the boundary stabilisation of a beam equation with boundary disturbance ⋮ Performance boundary output tracking for a wave equation with control unmatched disturbance ⋮ Static feedback stabilization of a rotating disk-cable system with measurements from each boundary ⋮ Anti-collocated observer-based output feedback control of wave equation with cubic velocity nonlinear boundary and Dirichlet control ⋮ Output feedback stabilization of an unstable wave equation with general corrupted boundary observation ⋮ The Lyapunov approach to boundary stabilization of an anti-stable one-dimensional wave equation with boundary disturbance

Cites Work

• Unnamed Item
• Unnamed Item
• Energie decay estimates and exact boundary value controllability for the wave equation in a bounded domain
• Stability results for the wave equation with indefinite damping
• A direct method for the boundary stabilization of the wave equation
• Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions
• Output-feedback stabilization of an unstable wave equation
• Backstepping observers for a class of parabolic PDEs
• Stabilization of the wave equation by on-off and positive-negative feedbacks
• Closed-Form Boundary State Feedbacks for a Class of 1-D Partial Integro-Differential Equations

This page was built for publication: Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary