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 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.

scholarly journals Further Results on Reachable Set Bounding for Discrete-Time System with Time-Varying Delay and Bounded Disturbance Inputs

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Wei Kang ◽  
Hao Chen ◽  
Kaibo Shi ◽  
Jun Cheng
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Reachable Set ◽  
Time Varying ◽  
Discrete Time System ◽  
Initial State ◽  
Time System ◽  
Time Varying Delay ◽  
Bounded Disturbance ◽  
Varying Delay

This paper investigates the problem of reachable set bounding for discrete-time system with time-varying delay and bounded disturbance inputs. Together with a new Lyapunov-Krasovskii functional, discrete Wirtinger-based inequality, and reciprocally convex approach, sufficient conditions are derived to find an ellipsoid to bound the reachable sets of discrete-time delayed system. The main advantage of this paper lies in two aspects: first, the initial state vectors are not necessarily zero; second, the obtained criteria in this paper do not really require all the symmetric matrices involved in the employed Lyapunov-Krasovskii functional to be positive definite. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

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 Stability of Stochastic Discrete-Time Neural Networks with Discrete Delays and the Leakage Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Liyuan Hou ◽  
Hong Zhu
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Delays ◽  
The Stability

This paper investigates the stability of stochastic discrete-time neural networks (NNs) with discrete time-varying delays and leakage delay. As the partition of time-varying and leakage delay is brought in the discrete-time system, we construct a novel Lyapunov-Krasovskii function based on stability theory. Furthermore sufficient conditions are derived to guarantee the global asymptotic stability of the equilibrium point. Numerical example is given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.

scholarly journals Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Discretization of Nonautonomous Nonlinear Systems Based on Continualization of an Exact Discrete-Time Model

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Triet Nguyen-Van ◽  
Noriyuki Hori
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Van Der Pol Oscillator ◽  
Discrete Time System ◽  
Time System ◽  
Time Model ◽  
Forward Difference ◽  
Discrete Time Models

An innovative approach is proposed for generating discrete-time models of a class of continuous-time, nonautonomous, and nonlinear systems. By continualizing a given discrete-time system, sufficient conditions are presented for it to be an exact model of a continuous-time system for any sampling periods. This condition can be solved exactly for linear and certain nonlinear systems, in which case exact discrete-time models can be found. A new model is proposed by approximately solving this condition, which can always be found as long as a Jacobian matrix of the nonlinear system exists. As an example of the proposed method, a van der Pol oscillator driven by a forcing sinusoidal function is discretized and simulated under various conditions, which show that the proposed model tends to retain such key features as limit cycles and space-filling oscillations even for large sampling periods, and out-performs the forward difference model, which is a well-known, widely-used, and on-line computable model.

scholarly journals Design of Optimal Output Regulators for Dual-Rate Linear Discrete-Time Systems Based on the Lifting Technique

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Yujian Guo ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Performance Index ◽  
Discrete Time System ◽  
Time System ◽  
Integer Multiple ◽  
Augmented System ◽  
Optimal Output ◽  
Lifting Technique ◽  
Discrete Time Systems ◽  
Time Systems

A design strategy of optimal output regulators for dual-rate discrete-time systems, whose output sampling period is an integer multiple of the input updating period, is proposed. At first, by using the discrete lifting technique, the dual-rate discrete-time system is converted to a single-rate augmented system in form and the lifted state-space model is constructed. Correspondingly, the performance index of the original system is modified to the performance index of the single-rate augmented system. And the original problem is transformed into an output regulation problem for the augmented system. Then, according to the optimal regulator theory, an optimal output regulator for the dual-rate discrete-time system is derived. In the meantime, the existence conditions of the optimal output regulator are discussed. Finally, a numerical example is included to illustrate the effectiveness of the proposed method.

Simple sufficient conditions for asymptotic stability of positive linear systems for any switchings

2013 ◽  
Vol 61 (2) ◽  
pp. 343-347 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Discrete Time System ◽  
Time System ◽  
Switched Linear Systems ◽  
Time Linear

Abstract The asymptotic stability of positive switched linear systems for any switchings is addressed. Simple sufficient conditions for the asymptotic stability of positive switched continuous-time and discrete-time linear systems are established. It is shown that the positive switched continuous-time (discrete-time) system is asymptotically stable for any switchings if the sum of entries of every column of the matrices of subsystems is negative (less than 1)

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