Control of 1-D parabolic PDEs with Volterra nonlinearities. I: Design

DOI10.1016/j.automatica.2008.04.013zbMath1152.93035OpenAlexW2084586390WikidataQ59621849 ScholiaQ59621849MaRDI QIDQ2377979

Rafael Vázquez, Krstić, Miroslav

Publication date: 20 January 2009

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2008.04.013

zbMATH Keywords

Lyapunov functionnonlinear controlboundary conditionsstabilizationdistributed parameter systemspartial differential equationsfeedback linearization

Mathematics Subject Classification ID

Related Items (30)

Control of 1D parabolic PDEs with Volterra nonlinearities. II: Analysis ⋮ Global finite-dimensional observer-based stabilization of a semilinear heat equation with large input delay ⋮ Guaranteed cost design for controlling semilinear parabolic PDE systems with mobile collocated actuators and sensors ⋮ Local stabilization of coupled nonlinear parabolic equations by boundary control ⋮ Null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach ⋮ Stabilization for the multi-dimensional heat equation with disturbance on the controller ⋮ Estimation of boundary parameters in general heterodirectional linear hyperbolic systems ⋮ Static output feedback stabilization for a linear parabolic PDE system with time-varying delay via mobile collocated actuator/sensor pairs ⋮ Boundary control of a coupled Burgers' PDE‐ODE system ⋮ Global stabilization of a 1D semilinear heat equation via modal decomposition and direct Lyapunov approach ⋮ Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction-diffusion PDEs on multidimensional balls ⋮ Flatness based trajectory planning and open-loop control of shallow-water waves in a tube ⋮ Backstepping control for the Schrödinger equation with an arbitrary potential in a confined space ⋮ Local exponential stabilization of Fisher's equation using the backstepping technique ⋮ Boundary Exponential Stabilization of 1-Dimensional Inhomogeneous Quasi-Linear Hyperbolic Systems ⋮ Optimal Time for the Controllability of Linear Hyperbolic Systems in One-Dimensional Space ⋮ Late-lumping backstepping control of partial differential equations ⋮ Nonlinear bilateral output-feedback control for a class of viscous Hamilton-Jacobi PDEs ⋮ Null-controllability of linear hyperbolic systems in one dimensional space ⋮ Lyapunov-based boundary feedback design for parabolic PDEs ⋮ Nonlinear control under wave actuator dynamics with time‐ and state‐dependent moving boundary ⋮ Boundary control and estimation of reaction–diffusion equations on the sphere under revolution symmetry conditions ⋮ Battery internal temperature estimation via a semilinear thermal PDE model ⋮ Small-Gain-Based Boundary Feedback Design for Global Exponential Stabilization of One-Dimensional Semilinear Parabolic PDEs ⋮ Explicit output-feedback boundary control of reaction-diffusion PDEs on arbitrary-dimensional balls ⋮ Global Stabilization of a Class of Nonlinear Reaction-Diffusion Partial Differential Equations by Boundary Feedback ⋮ Boundary feedback stabilization of the Schlögl system ⋮ Boundary observer design for a class of semi-linear hyperbolic PDE systems with recycle loop ⋮ Stability analysis of the anti-stable heat equation with uncertain disturbance on the boundary ⋮ Volterra series identification and its applications in structural identification of nonlinear block-oriented systems

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