scholarly journals Reduced-Orderl2−l∞Filter Design for a Class of Discrete-Time Nonlinear Systems with Multiple Sensor Faults

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Wenbai Li ◽  
Huxiong Li
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear System ◽  
Discrete Time ◽  
Sensor Faults ◽  
Reduced Order ◽  
Fuzzy Linear System ◽  
Multiple Sensor ◽  
Error System ◽  
Takagi Sugeno

The reduced-order filtering problem for a class of discrete-time smooth nonlinear systems subject to multiple sensor faults is studied. It is well known that a smooth complex nonlinear system can be approximated by a Takagi-Sugeno fuzzy linear system with finite number of subsystems. In this work, firstly, the discrete-time smooth nonlinear system is transferred into a Takagi-Sugeno fuzzy linear system with finite number of subsystems. Secondly, a filter with the reduced order of the original system is proposed to be designed. Different from the traditional assumption in which the measurement of the output is ideal, the measurement of the output is subject to sensor faults which are described via Bernoulli processes. By using the augmentation technique, a stochastic Takagi-Sugeno filtering error system is obtained. For the stochastic filtering error system, the exponential stability and the energy-to-peak performance are investigated. Sufficient conditions which can guarantee the exponential stability and thel2−l∞performance are obtained. Then, with the proposed conditions, the design procedure of the filter for the nonlinear system is proposed. Finally, a numerical example is used to show the effectiveness of the proposed design methodology.

scholarly journals Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Xiao Yu ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Tracking Error ◽  
Reference Signal ◽  
Original System ◽  
Linear Matrix ◽  
Preview Control ◽  
Lipschitz Nonlinear Systems ◽  
Error System ◽  
Discrete Integrator

This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.

scholarly journals Identification of Nonlinear Systems: Volterra Series Simplification

10.14311/976 ◽  
2007 ◽  
Vol 47 (4-5) ◽  
Author(s):  
A. Novák
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Transfer Function ◽  
Linear System ◽  
Impulse Response ◽  
Volterra Series ◽  
Series Representation ◽  
Multimedia Systems ◽  
Audio Amplifier ◽  
Enormous Number

Traditional measurement of multimedia systems, e.g. linear impulse response and transfer function, are sufficient but not faultless. For these methods the pure linear system is considered and nonlinearities, which are usually included in real systems, are disregarded. One of the ways to describe and analyze a nonlinear system is by using Volterra Series representation. However, this representation uses an enormous number of coefficients. In this work a simplification of this method is proposed and an experiment with an audio amplifier is shown. 

Takagi–Sugeno Fuzzy Predictive Control for a Class of Nonlinear System With Constrains and Disturbances

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Bin Wang ◽  
Jianwei Zhang ◽  
Delan Zhu ◽  
Diyi Chen
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Predictive Control ◽  
Three Dimensional ◽  
Fuzzy Model ◽  
Control Input ◽  
Chen System ◽  
External Disturbances ◽  
Takagi Sugeno ◽  
Fuzzy Predictive Control

This paper investigates the fuzzy predictive control for a class of nonlinear system with constrains under the condition of noise. Based on the fuzzy linearization theory, a class of nonlinear systems can be described by the Takagi–Sugeno (T–S) fuzzy model. The T–S fuzzy model and predictive control are combined to stabilize the proposed class of nonlinear system, and the detailed mathematical derivation is given. Moreover, the designed controller has been optimized even if the system is constrained by output and control input, or perturbed by external disturbances. Finally, numerical simulations including three-dimensional Lorenz system, four-dimensional Chen system and five-dimensional nonlinear system with external disturbances are presented to demonstrate the universality and effectiveness of the proposed scheme. The approach proposed in this paper is simple and easy to implement and also provides reference for relevant nonlinear systems.

scholarly journals Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 281-288
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Error Dynamics

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

scholarly journals Stable Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Model-Based Control Systems via Linear Matrix Inequalities: Three Conical Tank Case Study

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2221 ◽  
Author(s):  
Himanshukumar R. Patel ◽  
Vipul A. Shah
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Systems ◽  
Linear Models ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Takagi Sugeno

This paper deals with a methodical design approach of fault-tolerant controller that gives assurance for the the stabilization and acceptable control performance of the nonlinear systems which can be described by Takagi–Sugeno (T–S) fuzzy models. Takagi–Sugeno fuzzy model gives a unique edge that allows us to apply the traditional linear system theory for the investigation and blend of nonlinear systems by linear models in a different state space region. The overall fuzzy model of the nonlinear system is obtained by fuzzy combination of the all linear models. After that, based on this linear model, we employ parallel distributed compensation for designing linear controllers for each linear model. Also this paper reports of the T–S fuzzy system with less conservative stabilization condition which gives decent performance. However, the controller synthesis for nonlinear systems described by the T–S fuzzy model is a complicated task, which can be reduced to convex problems linking with linear matrix inequalities (LMIs). Further sufficient conservative stabilization conditions are represented by a set of LMIs for the Takagi–Sugeno fuzzy control systems, which can be solved by using MATLAB software. Two-rule T–S fuzzy model is used to describe the nonlinear system and this system demonstrated with proposed fault-tolerant control scheme. The proposed fault-tolerant controller implemented and validated on three interconnected conical tank system with two constraints in terms of faults, one issed to build the actuator and sond is system component (leak) respectively. The MATLAB Simulink platform with linear fuzzy models and an LMI Toolbox was used to solve the LMIs and determine the controller gains subject to the proposed design approach.

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