scholarly journals Boundary feedback control of an anti-stable wave equation

2020 ◽  
Vol 37 (4) ◽  
pp. 1367-1399
Author(s):  
Pierre APKARIAN ◽  
Dominikus NOLL
Keyword(s):  
Wave Equation ◽  
Output Feedback ◽  
Closed Loop ◽  
Dimensional System ◽  
Torsional Vibrations ◽  
Feedback Controllers ◽  
Boundary Feedback Control ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Infinite Dimensional System

Abstract We discuss boundary control of a wave equation with a non-linear anti-damping boundary condition. We design structured finite-dimensional $H_{\infty }$-output feedback controllers that stabilize the infinite-dimensional system exponentially in closed loop. The method is applied to control torsional vibrations in drilling systems with the goal to avoid slip-stick.

DYNAMICAL BEHAVIOR OF THE ALMOST-PERIODIC DISCRETE FITZHUGH–NAGUMO SYSTEMS

2007 ◽  
Vol 17 (05) ◽  
pp. 1673-1685 ◽  
Author(s):  
BIXIANG WANG
Keyword(s):  
Dynamical Behavior ◽  
Upper Semicontinuity ◽  
Dimensional System ◽  
Almost Periodic ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
All Solutions ◽  
Uniform Attractors ◽  
Infinite Lattices ◽  
Infinite Dimensional System

In this paper, we study the dynamical behavior of nonautonomous, almost-periodic discrete FitzHugh–Nagumo system defined on infinite lattices. We prove that the nonautonomous infinite-dimensional system has a uniform attractor which attracts all solutions uniformly with respect to the translations of external terms. We also establish the upper semicontinuity of uniform attractors when the infinite-dimensional system is approached by a family of finite-dimensional systems. This paper is based on a uniform tail method, which shows that, for large time, the tails of solutions are uniformly small with respect to bounded initial data as well as the translations of external terms. The uniform tail estimates play a crucial role for proving the uniform asymptotic compactness of the system and the upper semicontinuity of attractors.

scholarly journals Transfer operators for coupled analytic maps

2000 ◽  
Vol 20 (1) ◽  
pp. 109-143 ◽  
Author(s):  
TORSTEN FISCHER ◽  
HANS HENRIK RUGH
Keyword(s):  
Probability Measure ◽  
Banach Spaces ◽  
Dimensional System ◽  
Circle Maps ◽  
Infinite Dimensional ◽  
Transfer Operators ◽  
Finite Dimensional ◽  
Exponential Decay Of Correlations ◽  
Analytic Maps ◽  
Infinite Dimensional System

We consider analytically coupled circle maps (uniformly expanding and analytic) on the ${\mathbb Z}^d$-lattice with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures whose finite-dimensional marginals have analytic, exponentially bounded densities. Using residue calculus and ‘cluster expansion’-like techniques we define transfer operators on these Banach spaces. We get a unique (in the considered Banach spaces) probability measure that exhibits exponential decay of correlations.

scholarly journals Eliminating Impulse for Descriptor System by Derivative Output Feedback

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Jian Li ◽  
Yufa Teng ◽  
Qingling Zhang ◽  
Jinghao Li ◽  
Liang Qiao
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Descriptor System ◽  
Closed Loop System ◽  
Feedback Controllers ◽  
Matrix Pencils ◽  
System Equivalence ◽  
Dynamical Order ◽  
Theoretical Results

The problem of impulse elimination for descriptor system by derivative output feedback is investigated in this paper. Based on a novelly restricted system equivalence between matrix pencils, the range of dynamical order of the resultant closed loop descriptor system is given. Then, for the different dynamical order, sufficient conditions for the existence of derivative output feedback to ensure the resultant closed loop system to be impulse free are derived, and the corresponding derivative output feedback controllers are provided. Finally, simulation examples are given to show the consistence with the theoretical results obtained in this paper.

Predictor Feedback of Uncertain Single-Input Systems

2020 ◽  
pp. 235-266
Author(s):  
Yang Zhu ◽  
Miroslav Krstic
Keyword(s):  
Output Feedback ◽  
State Feedback ◽  
System Matrix ◽  
Unknown Parameters ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Linear Plant ◽  
Single Input ◽  
Distributed Actuator

This chapter presents the predictor feedback for uncertain single-input systems. This is based on the predictor feedback framework for uncertainty-free single-input systems in the previous chapter. The chapter addresses the five combinations of the five uncertainties that come from a single-input linear plant with distributed actuator delay. These uncertainties include the following types: unknown delay, unknown delay kernel, unknown parameters in the system matrix, unmeasurable finite-dimensional plant state, and unmeasurable infinite-dimensional actuator state. The chapter then studies adaptive state feedback under unknown delay, delay kernel, and parameter. It also assesses robust output feedback under unknown delay, delay kernel, and PDE or ODE state.

An adaptive multimodal approach to nonlinear sloshing in a rectangular tank

2001 ◽  
Vol 432 ◽  
pp. 167-200 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fluid Motion ◽  
Dimensional System ◽  
Infinite Dimensional ◽  
Modal Theory ◽  
Nonlinear Sloshing ◽  
Rectangular Tank ◽  
Wide Range ◽  
Infinite Dimensional System

Two-dimensional nonlinear sloshing of an incompressible fluid with irrotational flow in a rectangular tank is analysed by a modal theory. Infinite tank roof height and no overturning waves are assumed. The modal theory is based on an infinite-dimensional system of nonlinear ordinary differential equations coupling generalized coordinates of the free surface and fluid motion associated with the amplitude response of natural modes. This modal system is asymptotically reduced to an infinite-dimensional system of ordinary differential equations with fifth-order polynomial nonlinearity by assuming sufficiently small fluid motion relative to fluid depth and tank breadth. When introducing inter-modal ordering, the system can be detuned and truncated to describe resonant sloshing in different domains of the excitation period. Resonant sloshing due to surge and pitch sinusoidal excitation of the primary mode is considered. By assuming that each mode has only one main harmonic an adaptive procedure is proposed to describe direct and secondary resonant responses when Moiseyev-like relations do not agree with experiments, i.e. when the excitation amplitude is not very small, and the fluid depth is close to the critical depth or small. Adaptive procedures have been established for a wide range of excitation periods as long as the mean fluid depth h is larger than 0.24 times the tank breadth l. Steady-state results for wave elevation, horizontal force and pitch moment are experimentally validated except when heavy roof impact occurs. The analysis of small depth requires that many modes have primary order and that each mode may have more than one main harmonic. This is illustrated by an example for h/l = 0.173, where the previous model by Faltinsen et al. (2000) failed. The new model agrees well with experiments.

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