Positive Stabilization of a Diffusion System by Nonnegative Boundary Control

2017 ◽  
pp. 179-190 ◽  
Author(s):  
Jonathan N. Dehaye ◽  
Joseph J. Winkin
Keyword(s):  
Boundary Control ◽  
Diffusion System

Analytical solution of a hyperbolic partial differential equation and its application

2017 ◽  
Vol 10 (2) ◽  
pp. 183-199 ◽  
Author(s):  
Ping He ◽  
Yangmin Li
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Boundary Control ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Hyperbolic Partial Differential Equation ◽  
Hyperbolic Pde ◽  
Content Type

Purpose The purpose of this paper is to investigate the analytical solution of a hyperbolic partial differential equation (PDE) and its application. Design/methodology/approach The change of variables and the method of successive approximations are introduced. The Volterra transformation and boundary control scheme are adopted in the analysis of the reaction-diffusion system. Findings A detailed and complete calculation process of the analytical solution of hyperbolic PDE (1)-(3) is given. Based on the Volterra transformation, a reaction-diffusion system is controlled by boundary control. Originality/value The introduced approach is interesting for the solution of hyperbolic PDE and boundary control of the reaction-diffusion system.

Neumann Boundary Control of a Linear Diffusion System Based on the Equivalent Distributed Control Model

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Dyhia Hamdadou ◽  
Ahmed Maidi ◽  
Jean-Pierre Corriou
Keyword(s):  
Boundary Control ◽  
Control Strategy ◽  
Neumann Boundary ◽  
State Equation ◽  
Diffusion System ◽  
Linear Diffusion ◽  
Finite Characteristic ◽  
Loop Control ◽  
Characteristic Index ◽  
Point Tracking

Abstract This paper deals with the boundary control of a one-dimensional diffusion system with Neumann actuation. The objective is to control a given punctual output. The control design is based on the concept of the characteristic index from geometric control theory. The idea consists of making the boundary condition homogeneous by inserting the manipulated variable into the state equation using a proposed linear transformation. Then, in order to overcome the controllability problem and to have a finite characteristic index, a weighted value of the system state, along the spatial domain, is considered as an auxiliary output. By calculating the successive derivatives of the measured output, a state feedback that enforces a set point tracking of the measured output is developed. The stability of the resulting closed-loop control system is demonstrated based on Lyapunov's method. Then, in order to meet the desired control objective of the punctual output, a control strategy is proposed based on the steady-state analysis. The tracking performance of the developed control strategy is evaluated through numerical simulation by considering the temperature control of a thin metal rod modeled by a linear heat equation.

Sign in / Sign up

Export Citation Format

Share Document