Adaptive linear control interpreted as nonlinear dynamical feedback for nonlinear systems

2006 ◽  
pp. 366-376
Author(s):  
David J. Hill ◽  
Changyun Wen
Keyword(s):  
Nonlinear Systems ◽  
Linear Control ◽  
Nonlinear Dynamical

Carathe´odory Controllability Criterion for Nonlinear Dynamical Systems

1978 ◽  
Vol 100 (3) ◽  
pp. 209-213 ◽  
Author(s):  
G. Langholz ◽  
M. Sokolov
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Control Theory ◽  
Linear Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Modern Control Theory ◽  
Open Question ◽  
Modern Control

The question of whether a system is controllable or not is of prime importance in modern control theory and has been actively researched in recent years. While it is a solved problem for linear systems, it is still an open question when dealing with bilinear and nonlinear systems. In this paper, a controllability criterion is established based on a theorem by Carathe´odory. By associating a given dynamical system with a certain Pfaffian equation, it is argued that the system is controllable (uncontrollable) if its associated Pfaffian form is nonintegrable (integrable).

scholarly journals A Review of Phase Space Topology Methods for Vibration-Based Fault Diagnostics in Nonlinear Systems

2019 ◽  
Vol 8 (3) ◽  
pp. 393-401 ◽  
Author(s):  
T. Haj Mohamad ◽  
Foad Nazari ◽  
C. Nataraj
Keyword(s):  
Phase Space ◽  
Nonlinear Systems ◽  
Dynamic Systems ◽  
Dynamical Behavior ◽  
Fault Diagnostics ◽  
Nonlinear Dynamical ◽  
Space Topology ◽  
Nonlinear Features ◽  
Phase Space Topology

Abstract Background In general, diagnostics can be defined as the procedure of mapping the information obtained in the measurement space to the presence and magnitude of faults in the fault space. These measurements, and especially their nonlinear features, have the potential to be exploited to detect changes in dynamics due to the faults. Purpose We have been developing some interesting techniques for fault diagnostics with gratifying results. Methods These techniques are fundamentally based on extracting appropriate features of nonlinear dynamical behavior of dynamic systems. In particular, this paper provides an overview of a technique we have developed called Phase Space Topology (PST), which has so far displayed remarkable effectiveness in unearthing faults in machinery. Applications to bearing, gear and crack diagnostics are briefly discussed.

Optimal trajectories and linear control of nonlinear systems

AIAA Journal ◽  
1964 ◽  
Vol 2 (8) ◽  
pp. 1371-1379 ◽  
Author(s):  
ANDREW H. JAZWINSKI
Keyword(s):  
Nonlinear Systems ◽  
Linear Control ◽  
Optimal Trajectories

PREDICTIVE CONTROL OF NONLINEAR SYSTEMS BASED ON IDENTIFICATION BY BACKPROPAGATION NETWORKS

1994 ◽  
Vol 05 (04) ◽  
pp. 335-344 ◽  
Author(s):  
JIANBIN HAO ◽  
JOOS VANDEWALLE ◽  
SHAOHUA TAN
Keyword(s):  
Nonlinear Systems ◽  
Predictive Control ◽  
Neural Control ◽  
Nonlinear Dynamical Systems ◽  
Universal Approximation ◽  
Backpropagation Algorithm ◽  
Nonlinear Dynamical ◽  
Control Scheme ◽  
One Step ◽  
Simulation Results

Using the property of universal approximation of multilayer perceptron neural network, a class of discrete nonlinear dynamical systems are modeled by a perceptron with two hidden layers. A backpropagation algorithm is then used to train the model to identify the nonlinear systems to a desired level of accuracy. Based on the identified model, a one-step-ahead predictive control scheme is proposed in which the future control inputs are obtained through some nonlinear optimization process. Making use of the online learning properties of neural networks, the predictive control scheme is further developed into an adaptive one which is robust to the incompleteness of identification. Simulation results show that this neural control scheme works well even for some very complicated nonlinear systems.

Adaptive linear control of nonlinear systems

1990 ◽  
Vol 35 (11) ◽  
pp. 1253-1257 ◽  
Author(s):  
C. Wen ◽  
D.J. Hill
Keyword(s):  
Nonlinear Systems ◽  
Linear Control

Vibration Control Applied in a Semi-Active Suspension Using Magneto Rheological Damper and Optimal Linear Control Design

2013 ◽  
Vol 464 ◽  
pp. 229-234 ◽  
Author(s):  
Bruno Sousa Carneiro da Cunha ◽  
Fábio Roberto Chavarette
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Control Design ◽  
Mr Damper ◽  
Active Suspension ◽  
Linear Control ◽  
Linear Feedback ◽  
Optimal Linear ◽  
Magneto Rheological ◽  
Non Linear System

In this paper we study the behavior of a semi-active suspension witch external vibrations. The mathematical model is proposed coupled to a magneto rheological (MR) damper. The goal of this work is stabilize of the external vibration that affect the comfort and durability an vehicle, to control these vibrations we propose the combination of two control strategies, the optimal linear control and the magneto rheological (MR) damper. The optimal linear control is a linear feedback control problem for nonlinear systems, under the optimal control theory viewpoint We also developed the optimal linear control design with the scope in to reducing the external vibrating of the nonlinear systems in a stable point. Here, we discuss the conditions that allow us to the linear optimal control for this kind of non-linear system.

Observer-Based Piecewise Multi-Linear Controller Designs for Nonlinear Systems Using Feedback and Observer Linearizations

2020 ◽  
Vol 24 (1) ◽  
pp. 12-25
Author(s):  
Tadanari Taniguchi ◽  
Michio Sugeno ◽  
◽  
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Approximation ◽  
Linear Control ◽  
Separation Principle ◽  
Robust Observer ◽  
Linear Controller ◽  
Modeling Errors ◽  
Tracking Controller ◽  
Piecewise Model ◽  
Linear Controllers

This paper proposes observer-based piecewise multi-linear controllers for nonlinear systems using feedback and observer linearizations. The piecewise model is a nonlinear approximation and fully parametric. Feedback linearizations are applied to stabilize the piecewise multi-linear control system. Furthermore, observer linearizations are more conservative in modeling errors compared with feedback linearizations. In this paper, we propose robust observer designs for piecewise multi-linear systems. Moreover, we design piecewise multi-linear controllers that combine the robust observer with various performance such as a regulator and tracking controller. These design methods realize a separation principle that allows an observer and a regulator to be designed separately. Examples are demonstrated through computer simulation to confirm the feasibility of our proposals.

scholarly journals Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Min Wu ◽  
Zhengfeng Yang ◽  
Wang Lin
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Region Of Attraction ◽  
Nonlinear Dynamical ◽  
Recovery Techniques ◽  
Regions Of Attraction

We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.

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