Journal ArticleDOI
Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input
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This work designs and proves exponential stability of the origin of the resulting plant-observer-controller system in the spatial L2-sense, and solves the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and one leftward conve CTD.Abstract:
We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and one leftward convecting transport PDE. We design a controller, which requires a single control input applied on the leftward convecting PDE's right boundary, and an observer, which employs a single sensor on the same PDE's left boundary. We prove exponential stability of the origin of the resulting plant-observer-controller system in the spatial L2-sense.read more
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Stability and Boundary Stabilization of 1-D Hyperbolic Systems
Georges Bastin,Jean-Michel Coron +1 more
TL;DR: In this paper, the authors explore the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations and demonstrate the use of Lyapunov functions in this type of analysis.
Journal ArticleDOI
Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs
TL;DR: This paper presents a solution to the fully general case, in which the number of PDEs in either direction is arbitrary, and where actuation is applied on only one boundary, and solves the problem of control of coupled “homodirectional” hyperbolic linear PDE s, where multiple transport PDES convect in the same direction with arbitrary local coupling.
Journal ArticleDOI
Boundary control of coupled reaction-diffusion processes with constant parameters
TL;DR: Capabilities of the proposed synthesis and its effectiveness are supported by numerical studies made for three coupled systems with distinct diffusivity parameters and for underactuated linearized dimensionless temperature-concentration dynamics of a tubular chemical reactor, controlled through a boundary at low fluid superficial velocities when convection terms become negligible.
Journal ArticleDOI
Stabilization of coupled linear heterodirectional hyperbolic PDE–ODE systems
TL;DR: The problem of stabilizing a linear ODE having a system of a linearly coupled hyperbolic PDEs in the actuating and sensing paths is solved by mapping it to a target system with a cascade structure using a Volterra transformation.
Journal ArticleDOI
Finite-time output regulation for linear 2×2 hyperbolic systems using backstepping
TL;DR: The backstepping design of output feedback regulators for boundary controlled linear 2×2 hyperbolic systems, that achieve regulation in finite time, is presented and a finite-time output feedback regulator is obtained.
References
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Journal ArticleDOI
Mathematical Analysis and Numerical Methods for Science and Technology
TL;DR: These six volumes as mentioned in this paper compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers.
Book
Control and Nonlinearity
TL;DR: In this article, the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions are studied, with a focus on specific phenomena due to nonlinearities.
Analytical and Numerical Methods for Volterra Equations
TL;DR: Some applications of Volterraequations LinearVolterra equations of the second kind Nonlinear equations ofthe second kind Equations of the first kind Convolution equations The numerical solution of equations ofThe second kind.
Journal ArticleDOI
Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays
TL;DR: This work designs controllers using a backstepping method for parabolic PDEs and shows that the proposed method can be used for boundary control of the a Korteweg-de Vries-like third order PDE.