scholarly journals Design of preview controller for a type of discrete-time interconnected systems

2020 ◽  
Vol 53 (3-4) ◽  
pp. 719-729
Author(s):  
Hao Xie ◽  
Fucheng Liao ◽  
Usman ◽  
Jiamei Deng
Keyword(s):  
Discrete Time ◽  
Difference Operator ◽  
Interconnected Systems ◽  
Preview Control ◽  
Interconnected System ◽  
Lyapunov Function Method ◽  
System Equations ◽  
Error System ◽  
The Difference ◽  
Theoretical Results

This article proposes and studies a problem of preview control for a type of discrete-time interconnected systems. First, adopting the technique of decentralized control, isolated subsystems are constructed by splitting the correlations between the systems. Utilizing the difference operator to the system equations and error vectors, error systems are built. Then, the preview controller is designed for the error system of each isolated subsystem. The controllers of error systems of isolated subsystems are aggregated as a controller of the interconnected system. Finally, by employing Lyapunov function method and the properties of non-singular M-matrix, the guarantee conditions for the existence of preview controllers for interconnected systems are given. The numerical simulation shows that the theoretical results are effective.

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 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 Preview Tracking Control for Continuous-Time Singular Interconnected Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Hao Xie ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Numerical Simulation ◽  
Continuous Time ◽  
Tracking Control ◽  
Singular Systems ◽  
Tracking Error ◽  
Original System ◽  
Interconnected Systems ◽  
Interconnected System ◽  
Tracking Controller ◽  
Error System

This paper proposes and investigates a problem of preview tracking control for a class of continuous-time singular interconnected systems. Firstly, the related items are deleted to obtain several isolated subsystems with low dimensions. An error system is constructed for each isolated subsystem so that the tracking error is included in the state vector of the error system; then, the tracking problem is transformed into a regulation problem. Secondly, the preview tracking controller is designed for each error system and obtained controllers are combined as the controller of the error system of the singular interconnected system. Thirdly, the Lyapunov function method is utilized to determine the constraints of the related terms so that the closed-loop system of the error system of the singular interconnected system is stable under the action of the controller obtained. Finally, the preview tracking controller of the singular interconnected system is obtained from the relationship between the error system and the original system. A numerical simulation algorithm for continuous-time singular systems is also proposed in this paper. The numerical simulation illustrates the effectiveness of the theoretical results.

Design of a robust H∞ preview controller for a class of uncertain discrete-time systems

2017 ◽  
Vol 40 (8) ◽  
pp. 2639-2650 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Reference Signal ◽  
Lyapunov Stability Theory ◽  
Interference Rejection ◽  
Discrete Time Systems ◽  
Controller Gain ◽  
Error System ◽  
The Difference ◽  
System States ◽  
Time Systems

The robust preview tracking control problem of uncertain discrete-time systems satisfying matching conditions is considered. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to derive an augmented error system that includes the future information on the reference signal and disturbance signal to transform the tracking problem into a regulator problem. Then, a robust preview controller of the augmented error system is proposed by integrating Lyapunov stability theory and LMI approach. Research shows that the preview controller gain matrix can be determined by solving a LMI. The proposed robust preview controller in this paper cannot only guarantee the asymptotic stability of the closed-loop system, but also enhance the interference rejection properties. An integrator is applied to make sure that the output tracks the reference signal with no static error. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.

Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term

2020 ◽  
Vol 70 (5) ◽  
pp. 1165-1182
Author(s):  
George E. Chatzarakis ◽  
George M. Selvam ◽  
Rajendran Janagaraj ◽  
George N. Miliaras
Keyword(s):  
Fractional Order ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Damping Term ◽  
Transformation Technique ◽  
Order Difference ◽  
Numerical Examples ◽  
Oscillation Criteria ◽  
The Difference ◽  
Theoretical Results

AbstractThe aim in this work is to investigate oscillation criteria for a class of nonlinear discrete fractional order equations with damping term of the form$$\begin{array}{} \displaystyle \Delta\left[a(t)\left[\Delta\left(r(t)g\left(\Delta^\alpha x(t)\right)\right)\right]^\beta\right]+p(t)\left[\Delta\left(r(t)g\left(\Delta^\alpha x(t)\right)\right)\right]^\beta+F(t,G(t))=0, t\in N_{t_0}. \end{array}$$In the above equation α (0 < α ≤ 1) is the fractional order, $\begin{array}{} \displaystyle G(t)=\sum\limits_{s=t_0}^{t-1+\alpha}\left(t-s-1\right)^{(-\alpha)}x(s) \end{array}$ and Δα is the difference operator of the Riemann-Liouville (R-L) derivative of order α. We establish some new sufficient conditions for the oscillation of fractional order difference equations with damping term based on a Riccati transformation technique and some inequalities. We provide numerical examples to illustrate the validity of the theoretical results.

Stability of Large-Scale Fuzzy Interconnected System

2017 ◽  
pp. 11-33
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Large Scale ◽  
Stability Result ◽  
Interconnected Systems ◽  
Interconnected System ◽  
General Stability ◽  
Discrete Time Case ◽  
The Stability

This chapter studies the asymptotic stability of large-scale fuzzy interconnected systems. It firstly focused on the general stability analysis. Then, by using some bounding techniques, the fuzzy rules in interconnections to other subsystems are eliminated. Such condition leads to a reduced number of LMIs. Also, we will present the stability result for the discrete-time case. Finally, we give several examples to illustrate the use of corresponding results.

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 Partial Component Consensus of Discrete-Time Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Wenjun Hu ◽  
Gang Zhang ◽  
Zhongjun Ma ◽  
Binbin Wu
Keyword(s):  
Multiagent Systems ◽  
Discrete Time ◽  
Matrix Theory ◽  
Pinning Control ◽  
Directed Network ◽  
Strong Function ◽  
Partial Stability ◽  
Partial Component ◽  
The Matrix ◽  
Error System

The multiagent system has the advantages of simple structure, strong function, and cost saving, which has received wide attention from different fields. Consensus is the most basic problem in multiagent systems. In this paper, firstly, the problem of partial component consensus in the first-order linear discrete-time multiagent systems with the directed network topology is discussed. Via designing an appropriate pinning control protocol, the corresponding error system is analyzed by using the matrix theory and the partial stability theory. Secondly, a sufficient condition is given to realize partial component consensus in multiagent systems. Finally, the numerical simulations are given to illustrate the theoretical results.

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