Linear model matching with prescribed tracking error and internal stability for nonlinear systems

2006 ◽  
pp. 249-258 ◽  
Author(s):  
Christopher I. Byrnes ◽  
Rafael Castro ◽  
Alberto Isidori
Keyword(s):  
Nonlinear Systems ◽  
Linear Model ◽  
Tracking Error ◽  
Internal Stability ◽  
Model Matching

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

Iterative learning control algorithm for sensor fault nonlinear systems

2020 ◽  
pp. 1-8
Author(s):  
Zimian Lan
Keyword(s):  
Nonlinear Systems ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Tracking Error ◽  
Learning Control ◽  
Open Loop ◽  
Iterative Learning ◽  
Sensor Fault ◽  
Initial State ◽  
Control Gain

In this paper, we propose a new iterative learning control algorithm for sensor faults in nonlinear systems. The algorithm does not depend on the initial value of the system and is combined with the open-loop D-type iterative learning law. We design a period that shortens as the number of iterations increases. During this period, the controller corrects the state deviation, so that the system tracking error converges to the boundary unrelated to the initial state error, which is determined only by the system’s uncertainty and interference. Furthermore, based on the λ norm theory, the appropriate control gain is selected to suppress the tracking error caused by the sensor fault, and the uniform convergence of the control algorithm and the boundedness of the error are proved. The simulation results of the speed control of the injection molding machine system verify the effectiveness of the algorithm.

scholarly journals Internal Stability and L2 Gain of Nonlinear Systems

1993 ◽  
Vol 29 (6) ◽  
pp. 659-667 ◽  
Author(s):  
Junichi IMURA ◽  
Toshiharu SUGIE ◽  
Tsuneo YOSHIKAWA
Keyword(s):  
Nonlinear Systems ◽  
Internal Stability ◽  
L2 Gain

scholarly journals Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

2003 ◽  
Vol 125 (2) ◽  
pp. 170-177 ◽  
Author(s):  
Lili Wang ◽  
Jinghui Zhang ◽  
Chao Wang ◽  
Shiyue Hu
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear Model ◽  
Frequency Analysis ◽  
Nonlinear Behavior ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Vibration Data ◽  
Identification Technique ◽  
Stiffness And Damping

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

scholarly journals A Symbolic Computation Approach to Parameterizing Controller for Polynomial Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Cao ◽  
Xiaorong Hou
Keyword(s):  
Nonlinear Systems ◽  
Hamiltonian Systems ◽  
Symbolic Computation ◽  
External Disturbance ◽  
Disturbance Attenuation ◽  
Internal Stability ◽  
Parameterization Method ◽  
Numerical Example ◽  
Isaacs Equations ◽  
Controller Parameterization

This paper considers controller parameterization method ofH∞control for polynomial Hamiltonian systems (PHSs), which involves internal stability and external disturbance attenuation. The aims of this paper are to design a controller with parameters to insure that the systems areH∞stable and propose an algorithm for solving parameters of the controller with symbolic computation. The proposed parameterization method avoids solving Hamilton-Jacobi-Isaacs equations, and thus the obtained controllers with parameters are relatively simple in form and easy in operation. Simulation with a numerical example shows that the controller is effective as it can optimizeH∞control by adjusting parameters. All these results are expected to be of use in the study ofH∞control for nonlinear systems with perturbations.

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