Backstepping State Feedback Regulator Design for an Unstable Reaction-Diffusion PDE with Long Time Delay

2017 ◽  
Vol 24 (4) ◽  
pp. 563-576 ◽  
Author(s):  
Jian-Jun Gu ◽  
Jun-Min Wang
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Reaction Diffusion ◽  
Long Time ◽  
Feedback Regulator

scholarly journals State Feedback Regulation Problem to the Reaction-Diffusion Equation

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1983
Author(s):  
Francisco Jurado ◽  
Andrés A. Ramírez
Keyword(s):  
State Feedback ◽  
Feedback Regulation ◽  
Parabolic Type ◽  
Reaction Diffusion ◽  
The State ◽  
Reaction Diffusion Equation ◽  
Finite Dimensional ◽  
Sturm Liouville ◽  
Bounded Input ◽  
Feedback Regulator

In this work, we explore the state feedback regulator problem (SFRP) in order to achieve the goal for trajectory tracking with harmonic disturbance rejection to one-dimensional (1-D) reaction-diffusion (R-D) equation, namely, a partial differential equation of parabolic type, while taking into account bounded input, output, and disturbance operators, a finite-dimensional exosystem (exogenous system), and the state of the exosystem as the state to the feedback law. As is well-known, the SFRP can be solved only if the so-called Francis (regulator) equations have solution. In our work, we try with the solution of the Francis equations from the 1-D R-D equation following given criteria to the eigenvalues from the exosystem and transfer function of the system, but the state operator is here defined in terms of the Sturm–Liouville differential operator (SLDO). Within this framework, the SFRP is then solved for the 1-D R-D equation. The numerical simulation results validate the performance of the regulator.

Optimal State Feedback Control in Operator Domain for Multi-Rate Networked Control Systems with Long Time Delay

2012 ◽  
Vol 241-244 ◽  
pp. 1672-1676
Author(s):  
Yan Ping Wang ◽  
Qi Xin Zhu ◽  
Zhi Ping Li
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Control Systems ◽  
State Feedback ◽  
Networked Control Systems ◽  
State Feedback Control ◽  
Networked Control ◽  
Programming Approach ◽  
Operator Domain ◽  
Long Time

By multi-rate networked control systems (NCS), we mean the sampling periods of the sensor, the controller and the actuator in networked control systems are not the same, that is to say there are more than one sampling rate in networked control systems. For the long time delay multi-rate NCS with event-driven controller and actuator, a stochastic discrete model is established under operator. The state feedback control laws for the multi-rate NCS in operator domain are designed by using a dynamic programming approach. The derived optimal LQG controller can be used as a delay-compensator for multi-rate NCS with long time delays. An example is given to verify the theory results of this paper.

Long-time dynamics of a class of nonlocal extensible beams with time delay

2021 ◽  
pp. 108128652110194
Author(s):  
Fengjuan Meng ◽  
Cuncai Liu ◽  
Chang Zhang
Keyword(s):  
Time Delay ◽  
Stability Property ◽  
Beam Equation ◽  
Exponential Attractors ◽  
Time Dynamics ◽  
Bounded Smooth Domain ◽  
Finite Dimensional ◽  
Long Time ◽  
Bounded Smooth ◽  
Long Time Dynamics

This work is devoted to the following nonlocal extensible beam equation with time delay: [Formula: see text] on a bounded smooth domain [Formula: see text]. The main purpose of this paper is to consider the long-time dynamics of the system. Under suitable assumptions, the quasi-stability property of the system is established, based on which the existence and regularity of a finite-dimensional compact global attractor are obtained. Moreover, the existence of exponential attractors is proved.

Sign in / Sign up

Export Citation Format

Share Document