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 Optimal Preview Control for Discrete-Time Systems in Multirate Output Sampling

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Fucheng Liao ◽  
Yujian Guo
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Original System ◽  
Preview Control ◽  
Lifting Technique ◽  
Discrete Time Systems ◽  
Error System ◽  
Existence Conditions ◽  
Time Systems ◽  
Discrete Integrator

This paper studies the disturbance preview optimal control problem for discrete-time systems with multirate output sampling. By constructing the error system and using the discrete lifting technique, we reduce the multirate preview control problem to a single-rate one for a formal augmented system. Then, applying preview control theory, the optimal preview control law of the augmented error system is obtained. Meanwhile, we introduce a discrete integrator to eliminate the static error. Then we study a method to design a controller with preview action for the original system. And the existence conditions of the controller are also discussed in detail. Finally, numerical simulation is included to illustrate the effectiveness of the proposed method.

Design of an Optimal Preview Controller for Dual-Rate Linear Discrete-Time Systems

2018 ◽  
Vol 6 (2) ◽  
pp. 178-192 ◽  
Author(s):  
Yujian Guo ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Reference Signal ◽  
Sufficient Conditions ◽  
Original System ◽  
Discrete Time System ◽  
Linear Quadratic ◽  
Preview Control ◽  
Time System ◽  
Lifting Technique ◽  
Error System

Abstract A dual-rate preview control strategy for a type of discrete-time system is proposed based on the theory of multirate control. First, by using the discrete lifting technique, the general dual-rate discrete-time system is converted into a single-rate augmented system. On this basis, the augmented error system is constructed by introducing a first-order difference operator and the previewable reference signal. Then the tracking problem is transformed into a regulator problem of the augmented error system. The optimal preview control law of the augmented error system is obtained by using standard linear quadratic optimal preview control theory, and then the optimal preview controller of the original system is derived. In addition, the necessary and sufficient conditions for the controller are given. Finally, simulation results show the effectiveness of the proposed method.

scholarly journals Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Fucheng Liao ◽  
Yingxue Wu ◽  
Xiao Yu ◽  
Jiamei Deng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Tracking Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Error System ◽  
Finite Time Boundedness ◽  
Boundedness Problem ◽  
Time Systems

A finite-time bounded tracking control problem for a class of linear discrete-time systems subject to disturbances is investigated. Firstly, by applying a difference method to constructing the error system, the problem is transformed into a finite-time boundedness problem of the output vector of the error system. In fact, this is a finite-time boundedness problem with respect to the partial variables. Secondly, based on the partial stability theory and the research methods of finite-time boundedness problem, a state feedback controller formulated in form of linear matrix inequality is proposed. Based on this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is presented to illustrate the effectiveness of the controller.

scholarly journals Design of an Optimal Preview Controller for a Class of Linear Discrete-Time Descriptor Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Fucheng Liao ◽  
Zhihua Xue ◽  
Jiang Wu
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Original System ◽  
Simulation Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Equivalent Transformation ◽  
Normal System ◽  
Preview Control ◽  
Error System

The preview control problem of a class of linear discrete-time descriptor systems is studied. Firstly, the descriptor system is decomposed into a normal system and an algebraic equation by the method of the constrained equivalent transformation. Secondly, by applying the first-order forward difference operator to the state equation, combined with the error equation, the error system is obtained. The tracking problem is transformed into the optimal preview control problem of the error system. Finally, the optimal controller of the error system is obtained by using the related results and the optimal preview controller of the original system is gained. In this paper, we propose a numerical simulation method for descriptor systems. The method does not depend on the restricted equivalent transformation.

scholarly journals Design of a Preview Controller for Discrete-Time Systems Based on LMI

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Controller Design ◽  
Design Method ◽  
Reference Signal ◽  
Original System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Time Systems

A preview controller design method for discrete-time systems based on LMI is proposed. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to transform the tracking problem into a regulator problem. Then, based on the Lyapunov stability theory and linear matrix inequality (LMI) approach, the preview controller ensuring asymptotic stability of the closed-loop system for the derived augmented error system is found. And an extended functional observer is designed in this paper which can achieve disturbance attenuation in the estimation process; as a result, the state of the system can be reconstructed rapidly and accurately. The controller gain matrix is obtained by solving an LMI problem. By incorporating the controller obtained into the original system, we obtain the preview controller of the system under consideration. To make sure that the output tracks the reference signal without steady-state error, an integrator is introduced. The numerical simulation example also illustrates the effectiveness of the results in the paper.

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 Robust Preview Control for Uncertain Discrete Singular Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jiang Wu ◽  
Fucheng Liao ◽  
Yifan Shao ◽  
Shujie Gao ◽  
Hao Wang ◽  
...  
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Reference Signal ◽  
Linear Matrix ◽  
Preview Control ◽  
Forward Difference ◽  
Input Control ◽  
Discrete Singular Systems ◽  
Error System ◽  
The Stability

In this paper, the problem of robust preview control for uncertain discrete singular systems is considered. First of all, by employing the forward difference for uncertain discrete singular systems, the singular augmented error system with the state vector, the input control vector, and the previewable reference signal is derived. Since there is a singular matrix in the system, the existing method cannot be directly applied to this problem. By considering the stability of the transposition system with Linear Matrix Inequality (LMI) method, a new stability criterion for the transposition system is introduced. Then, the robust controller for the augmented error system is obtained, which is regarded as the robust preview controller for the original singular system. At last, the numerical simulation shows the correctness and effectiveness of the results.

New results on observer-based robust preview tracking control for Lipschitz nonlinear systems

2020 ◽  
pp. 107754632095365
Author(s):  
Xiao Yu ◽  
Fucheng Liao ◽  
Li Li
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Tracking Control ◽  
Reference Signal ◽  
State Feedback Control ◽  
Control Action ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Integral Control ◽  
Lipschitz Nonlinear Systems

In this article, the observer-based robust preview tracking control problem is revisited for discrete-time Lipschitz nonlinear systems. The proposed observer-based preview control scheme is composed of the integral control action, the observer-based state feedback control action, and the preview feedforward action of the reference signal. Sufficient design condition of controller and observer gains, which are able to ensure the simultaneously convergence of both the estimation error and the tracking error toward zero, is established in terms of linear matrix inequality by applying the Lyapunov function approach and several mathematical techniques. Compared with the existing result, the system model is more general, which could describe a larger range of practical processes. The observer-based preview controller design is simplified by computing the gain matrices of both observer and tracking controller simultaneously by only one-step linear matrix inequality procedure. Robustness against external disturbance is analyzed via the H∞ performance criterion to attenuate its effect on the performance signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the suggested controller.

Robust Tracking Control for a Class of Nonlinear Systems

2012 ◽  
Vol 479-481 ◽  
pp. 2161-2164
Author(s):  
Yang Yu ◽  
Wei Wang
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Tracking Error ◽  
Reference Signal ◽  
Linear Matrix ◽  
Robust Tracking ◽  
Robust Tracking Control ◽  
Controlled System ◽  
Stabilization Control ◽  
S Model

This paper deals with the problem of fizzy robust tracking control for a class of nonlinear systems. The nonlinear system is approximated by T-S model, considering the modeling error. The tracking error of the controlled system following the reference signal is studied, and the tracking error’s exponential stability. The coherence of tracking control and stabilization control of the fuzzy systems is proved by using Lyapunov function theory combining with linear matrix inequalities (LMIs).Simulation results demonstrate the effectiveness of the proposed approach and conditions.

Preview tracking control for a class of discrete-time Lipschitz non-linear time-delay systems

2018 ◽  
Vol 36 (3) ◽  
pp. 849-867 ◽  
Author(s):  
Xiao Yu ◽  
Fucheng Liao
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Linear Time ◽  
Reference Signal ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Memory State ◽  
Non Linear ◽  
Error System

AbstractThe design of a preview tracking controller for a class of discrete-time Lipschitz non-linear time-delay systems is considered in this paper. First, based on preview control theory, we introduce a difference operator and deduce an augmented error system which contains previewable information on the reference signal. The original tracking problem is thus transformed into a regulation problem. Second, we design a memory state feedback controller for the augmented error system. Applying Lyapunov’s second method, the sufficient condition for stability of the closed-loop system is derived in the form of linear matrix inequality (LMI), and the preview controller is obtained accordingly. Finally, to show the superiority of the controller proposed, two numerical examples are presented.

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