Direct Predictive Boundary Control of a First-order Quasilinear Hyperbolic PDE

2019 ◽  
Author(s):  
Timm Strecker ◽  
Ole Morten Aamo ◽  
Michael Cantoni
Keyword(s):  
Boundary Control ◽  
Hyperbolic Pde ◽  
First Order

Backstepping Boundary Control for First-Order Hyperbolic PDEs on Inverted Pendulum Stabilization with Constant Input Delay

2021 ◽  
Author(s):  
Arnab Pal ◽  
Ramashis Banerjee ◽  
Debottam Mukherjee ◽  
Samrat Chakraborty ◽  
Pabitra Kumar Guchhait ◽  
...  
Keyword(s):  
Boundary Control ◽  
Inverted Pendulum ◽  
Input Delay ◽  
Constant Input ◽  
Hyperbolic Pdes ◽  
First Order

scholarly journals Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Xin Yu ◽  
Chao Xu ◽  
Huacheng Jiang ◽  
Arthi Ganesan ◽  
Guojie Zheng
Keyword(s):  
Feedback Control ◽  
Integral Transformation ◽  
Original System ◽  
Open Loop ◽  
Hyperbolic Partial Differential Equations ◽  
Target System ◽  
Control Law ◽  
Hyperbolic Pde ◽  
First Order ◽  
Boundary Control Problems

This paper deals with the stabilization problem of first-order hyperbolic partial differential equations (PDEs) with spatial-temporal actuation over the full physical domains. We assume that the interior actuator can be decomposed into a product of spatial and temporal components, where the spatial component satisfies a specific ordinary differential equation (ODE). A Volterra integral transformation is used to convert the original system into a simple target system using the backstepping-like procedure. Unlike the classical backstepping techniques for boundary control problems of PDEs, the internal actuation can not eliminate the residual term that causes the instability of the open-loop system. Thus, an additional differential transformation is introduced to transfer the input from the interior of the domain onto the boundary. Then, a feedback control law is designed using the classic backstepping technique which can stabilize the first-order hyperbolic PDE system in a finite time, which can be proved by using the semigroup arguments. The effectiveness of the design is illustrated with some numerical simulations.

scholarly journals A boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions

2015 ◽  
Vol 4 (4) ◽  
pp. 311-325 ◽  
Author(s):  
Pierluigi Colli ◽  
Gianni Gilardi ◽  
Jürgen Sprekels
Keyword(s):  
Boundary Conditions ◽  
Control Problem ◽  
Boundary Control ◽  
Necessary Conditions ◽  
Dynamic Boundary Conditions ◽  
First Order ◽  
Boundary Control Problem ◽  
Dynamic Boundary ◽  
Necessary Conditions For Optimality ◽  
Cahn Hilliard Equation

AbstractA boundary control problem for the pure Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved.

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