Output Feedback Stabilization of the Linearized Bilayer Saint-Venant Model

2016 ◽  
Author(s):  
Ababacar Diagne ◽  
Shuxia Tang ◽  
Mamadou Diagne ◽  
Miroslav Krstic
Keyword(s):  
Output Feedback ◽  
Control Method ◽  
Coupled System ◽  
Backstepping Control ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Varying Coefficients ◽  
The One ◽  
Spatially Varying ◽  
Constant System

We consider the problem of output feedback exponentially stabilizing the 1-D bilayer Saint-Venant model, which is a coupled system of two rightward and two leftward convecting transport partial differential equations (PDEs). The PDE backstepping control method is employed. Our designed output feedback controller is based on the observer built in this paper and the state feedback controller designed in [1], where the backstepping control design idea can also be referred to [2] and can be treated as a generalization of the result for the system with constant system coefficients [2] to the one with spatially-varying coefficients. Numerical simulations of the bilayer Saint-Venant problem are also provided to verify the result.

scholarly journals Congestion Control Based on Multiple Model Adaptive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xinhao Yang ◽  
Ze Li
Keyword(s):  
Adaptive Control ◽  
Congestion Control ◽  
Output Feedback ◽  
Control Method ◽  
Feedback Controller ◽  
Multiple Model ◽  
Network Condition ◽  
Output Feedback Controller ◽  
Weight Calculation ◽  
Multiple Model Adaptive Control

The congestion controller based on the multiple model adaptive control is designed for the network congestion in TCP/AQM network. As the conventional congestion control is sensitive to the variable network condition, the adaptive control method is adopted in our congestion control. The multiple model adaptive control is introduced in this paper based on the weight calculation instead of the parameter estimation in past adaptive control. The model set is composed by the dynamic model based on the fluid flow. And three “local” congestion controllers are nonlinear output feedback controller based on variable RTT, H2output feedback controller, and proportional-integral controller, respectively. Ns-2 simulation results in section 4 indicate that the proposed algorithm restrains the congestion in variable network condition and maintains a high throughput together with a low packet drop ratio.

Boundary output feedback stabilization of transport equation with non-local term

2019 ◽  
Vol 37 (3) ◽  
pp. 752-764
Author(s):  
Liping Wang ◽  
Feng-Fei Jin
Keyword(s):  
Transport Equation ◽  
Output Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Closed Loop System ◽  
Output Feedback Stabilization ◽  
Exponentially Stable ◽  
Non Local ◽  
Local Term

Abstract In this paper, we are concerned with boundary output feedback stabilization of a transport equation with non-local term. First, a boundary state feedback controller is designed by a backstepping approach. The closed-loop system is proved to be exponentially stable by the equivalence between original and target system. Then, we design an output feedback controller based on an infinite-dimensional observer. It is shown that the result closed-loop system is also exponentially stable. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed feedback controller.

scholarly journals On the Practical Output Feedback Stabilization for Nonlinear Uncertain Systems

2009 ◽  
Vol 14 (2) ◽  
pp. 145-153 ◽  
Author(s):  
A. Benabdallah
Keyword(s):  
Output Feedback ◽  
Uncertain Systems ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Practical Stability ◽  
Closed Loop System ◽  
Output Feedback Controller ◽  
Output Feedback Stabilization ◽  
Nonlinear Uncertain Systems

In this paper, we treat the problem of output feedback stabilization of nonlinear uncertain systems. We propose an output feedback controller that guarantees global uniform practical stability of the closed loop system.

Introduction to the WKB(J) Approximation: All Things Airy

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Applied Mathematics ◽  
Approximate Solutions ◽  
Airy Functions ◽  
Linear Ordinary Differential Equations ◽  
Function Solution ◽  
Varying Coefficients ◽  
Derivative Term ◽  
Liouville Transformation ◽  
The One ◽  
Spatially Varying

This chapter deals with the WKB(J) approximation, commonly used in applied mathematics and mathematical physics to find approximate solutions of linear ordinary differential equations (of any order in principle) with spatially varying coefficients. The WKB(J) approximation is closely related to the semiclassical approach in quantum mechanics in which the wavefunction is characterized by a slowly varying amplitude and/or phase. The chapter first introduces an inhomogeneous differential equation, from which the first derivative term is eliminated, before discussing the Liouville transformation and the one-dimensional Schrödinger equation. It then presents a physical interpretation of the WKB(J) approximation and its application to a potential well. It also considers the “patching region” in which the Airy function solution (the local turning point) is valid, the relation between Airy functions and Bessel functions, Airy integral and related topics, and related integrals.

Nonlinear augmented state observer-based adaptive output feedback anti-disturbance control for nonlinear systems with non-harmonic multiple uncertainties

2018 ◽  
Vol 41 (7) ◽  
pp. 1904-1911 ◽  
Author(s):  
Weijun Hu
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Control Method ◽  
Experimental Studies ◽  
Nonlinear Damping ◽  
State Observer ◽  
Feedback Controller ◽  
Robust Adaptive ◽  
System States ◽  
Augmented State

In this paper, a novel output feedback anti-disturbance control method is carried out for a class of nonlinear systems subject to non-harmonic multisource disturbances. By using a nonlinear exogenous system, a class of non-harmonic disturbances possessing complex and nonlinear characteristics are taken fully into consideration. Based on a nonlinear damping term, we establish an adaptive augmented state observer that can achieve robust asymptotic disturbance estimation for the system states, the harmonic disturbances and the non-harmonic disturbances. By fusing the augmented state observer and a state-feedback controller, a robust adaptive output feedback anti-disturbance control structure is constructed. The boundness of the combined controller–observer system is derived on the basis of Lyapunov analysis. Furthermore, aiming at the intense non-harmonic disturbances, the proposed method is extended and a new output feedback controller is obtained. The effectiveness of the proposed scheme is demonstrated through experimental studies on a practical example.

Sign in / Sign up

Export Citation Format

Share Document