Stabilization of One-dimensional Wave Equation with Van Der Pol Type Boundary Condition

DOI10.1137/15M1045296zbMath1346.74100OpenAlexW2523040838MaRDI QIDQ2821805

Hongyinping Feng

Publication date: 23 September 2016

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1045296

zbMATH Keywords

Riesz basiswave equationstabilizationvan der Pol type boundary

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Control/observation systems governed by partial differential equations (93C20) Feedback control (93B52)

Related Items

Output feedback stabilization for 1-D wave equation with variable coefficients and non-collocated observation, A novel observer-based approach for the exponential stabilization of the string PDE with cubic nonlinearities, Delay compensation for regular linear systems, Anti-collocated observer-based output feedback control of wave equation with cubic velocity nonlinear boundary and Dirichlet control

Cites Work

• Unnamed Item
• Output-feedback adaptive control of a wave PDE with boundary anti-damping
• Arbitrary decay rate for two connected strings with joint anti-damping by boundary output feedback
• Active disturbance rejection control based on weighed-moving-average-state-observer
• Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary
• Uniform boundary controllability of a discrete 1-D wave equation
• The Lyapunov approach to boundary stabilization of an anti-stable one-dimensional wave equation with boundary disturbance
• Observer Design for Wave Equations with van der Pol Type Boundary Conditions
• Pointwise Stabilization in the Middle of the Span for Second Order Systems, Nonuniform and Uniform Exponential Decay of Solutions
• Chaotic vibrations of the one-dimensional wave equation due to a self-excitation boundary condition. Part I: Controlled hysteresis
• Asymptotic Behaviour of Solutions of the One-Dimensional Wave Equation with a Nonlinear Boundary Stabilizer
• Conditions for Robustness and Nonrobustness of the Stability of Feedback Systems with Respect to Small Delays in the Feedback Loop
• Chaotic Vibrations of the One-Dimensional Wave Equation due to a Self-Excitation Boundary Condition.
• Chaotic Vibrations of the One-Dimensional Wave Equation Due to a Self-Excitation Boundary Condition.
• The Stabilization of a One-Dimensional Wave Equation by Boundary Feedback With Noncollocated Observation
• Sliding Mode and Active Disturbance Rejection Control to Stabilization of One-Dimensional Anti-Stable Wave Equations Subject to Disturbance in Boundary Input