时变参数不确定离散时间系统的预见控制

基于具有参数依赖的Lyapunov函数方法及LMI技巧,研究一类时变参数不确定离散时间系统的预见跟踪控制问题.首先,采用预见控制理论中误差系统的方法,引入两个与状态变量和输入变量有关的辅助信号,构造出包含未来目标值信号和干扰信号的信息的扩大误差系统,将原系统的预见跟踪问题转化为扩大误差系统的镇定问题;然后,针对扩大误差系统,考虑输出反馈时,通过改造输出方程融合可预见信号的未来信息.研究表明,通过求解LMI,即可确定静态输出反馈预见控制器增益矩阵的参数矩阵.数值仿真表明了结果的有效性.     

不确定离散时滞系统的保性能预见控制

针对一类带有状态时滞的线性离散不确定系统,提出一种基于LMI的保性能预见控制器设计方法.首先引入差分算子,将时滞系统转换为一般系统,同时对可预见的未来目标值信号作差分处理,构造出包含未来目标值信息的扩大误差系统;其次引入保性能控制,导出扩大误差系统在相应性能指标下渐近稳定的充分条件;最后通过求解一个有LMI约束的优化问题,得到了系统的最优保性能预见控制律.     

线性连续时间时滞系统的有限时间有界跟踪控制

研究一类线性连续时间时滞系统的有限时间有界跟踪控制问题.首先,采用预见控制理论中求导的方法构造带有时滞的误差系统,把误差信号的信息包含在误差系统的状态向量中,再将其作为误差系统的输出向量;其次,通过为误差系统设计一个有记忆的状态反馈控制器,把问题转化为研究带有时滞的误差系统的闭环系统输入-输出有限时间稳定问题;再次,借鉴输入-输出有限时间稳定的研究方法和线性矩阵不等式的方法, 通过构造Lyapunov-Krasovskii函数,给出由一组线性矩阵不等式表征的控制器增益矩阵的设计方法,由此得到原系统的一个有限时间有界跟踪控制器;最后,通过一个数值实例验证所设计的控制器的有效性和优越性.     

周期离散时间系统的预见控制器设计

对于一类线性周期离散时间系统,提出一种新的周期预见控制器的设计方法.首先,利用二维模型方法及系数矩阵的周期性特点,将系统状态与其稳态值之差代替通常的状态差分,成功地构造出原系统的二维(2D)扩大误差系统;然后,针对导出的扩大误差系统,结合Lyapunov稳定性理论和LMI方法,给出闭环系统渐近稳定的条件及预见控制器的设计方法;最后,通过数值仿真说明该方法的有效性.     

具有外部扰动的离散广义系统有限时间控制

讨论一类具有有限能量的外部扰动的线性离散广义系统的有限时间控制问题。分析问题可解性,得到该问题可解的充分条件,通过状态反馈控制器和输出反馈控制器的设计,给出实现闭环系统有限时间有界的充分条件,这些充分条件可以转化为线性矩阵不等式(LMI)的可行解问题,可借助Matlab中的LMI工具箱求解,最后通过数值算例验证该方法的...     

一类线性离散时间系统有限时间控制问题

讨论一类具有时变、有限能量外部扰动的线性离散时间系统的有限时间控制问题.首先研究问题可解的充分条件,并讨论了状态反馈控制器存在的条件,这些条件可归结为基于线性矩阵不等式(LMI)的可解性问题;然后给出状态反馈控制器和输出反馈控制器的具体设计;最后通过仿真验证了该方案的有效性.     

不确定离散时间系统的有限时间预见跟踪控制

研究一类不确定离散时间系统的有限时间鲁棒预见控制问题.与以往对误差信号和系统方程取差分不同,通过引入辅助变量,并用系统状态向量及输入向量与相应辅助变量之差代替通常的状态差分,避免对时变的系数矩阵取差分,使得扩大误差系统的构造成为可能.另外,所推导的扩大误差系统不再包含误差向量,这不仅能降低系统的阶数而且能推广适用对象....     

多采样率不确定离散时滞系统的鲁棒预见控制

研究一类输入多采样率型不确定离散时滞系统的鲁棒预见控制问题.首先,利用离散提升技术从形式上消除输入时滞和多采样率特点,将多采样率不确定系统的鲁棒预见控制问题转化为一个普通的单采样率不确定系统的鲁棒预见控制问题;然后根据预见控制的基本方法,构造出包含未来目标信息的扩大误差系统,并对其相应的标称系统设计预见控制器;最后,根据所设计的控制器和Lyapunov稳定性理论,给出不确定闭环系统的鲁棒稳定性判据.数值仿真结果验证了所提出设计方法的有效性.     

离散T-S模糊系统的部分状态反馈H∞控制

基于部分状态信息的控制器是一类特殊的静态输出反馈控制器,一般难以利用线性矩阵不等式工具求解.本文研究离散T-S模糊系统的部分状态反馈镇定及部分状态反馈H∞控制问题.通过引入松弛变量,将离散T-S模糊系统的部分状态反馈镇定问题转换成求解一组线性矩阵不等式（LMI）,并给出基于LMI的部分状态反馈H∞控制器设计方法.通过数值算例验证了所给方法的有效性.     

时延不确定离散时间系统的鲁棒跟踪控制

研究一类时延不确定离散时间系统的鲁棒跟踪控制问题．基于线性矩阵不等式(LMI)的控制方法，设计无记忆反馈控制器，构造了适用于时延不确定离散时间系统的Lyapunov函数．通过求解一个LMI便可得到控制器的增益矩阵，从而使系统的状态变量渐近跟踪预先设定的轨迹．仿真示例说明所提出的鲁棒跟踪控制算法是有效的．     

Output feedback preview tracking control for discrete-time polytopic time-varying systems

This paper focuses on the problem of static output feedback preview tracking control for discrete-time systems with time-varying parameters subject to a previewable reference signal. We develop a design method of a robust controller with integral and preview actions achieving robust tracking performance. First, an augmented error system including future information on reference signal is constructed by introducing two new related auxiliary variables to the original system state and input. This leads to a tracking problem being transformed into a regulator problem. Then, a previewable reference signal is fully utilised through reformulation of the output equation for the augmented error system while considering a static output feedback. Meanwhile, the static output preview control gains are solved explicitly by the proposed conditions. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.     

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.     

Preview control of polytopic time-varying systems subject to actuator saturation

In this study, a novel method is proposed to track a previewable reference signal in the polytopic time-varying system with input saturation. Firstly, an augmented model containing future information is constructed using a new formal variable. This leads to the tracking control problem of polytopic time-varying system with input saturation is transformed into a stability problem of augmented error system. Next, the state and static output feedback preview controls are introduced, and the corresponding controller gains are produced by the proposed conditions. Two examples are presented to validate the effectiveness of the proposed preview controller.     

线性连续时滞系统最优预见重复控制

针对一类线性连续时滞系统,提出一种最优预见重复控制设计方法.首先,通过一种等价变换,将被控时滞系统转化为无时滞系统.然后,利用L阶差分算子提升技巧,获得包含状态变量导数和跟踪误差的增广连续系统.在此基础上,通过定义一种新的性能指标,将预见重复控制设计问题转化为连续非自治系统的线性二次调节问题.进一步,基于最优控制理论,得到包含状态反馈、误差积分、重复控制、时滞补偿和预见补偿的最优预见重复控制器.该控制器包含了已有文献的多种控制器形式.最后,通过一个数值仿真实例,说明所提方法的有效性.     

Finite-time stabilization via dynamic output feedback

In this paper the finite-time stabilization of continuous-time linear systems is considered; this problem has been previously solved in the state feedback case. In this work the assumption that the state is available for feedback is removed and the output feedback problem is investigated. The main result provided is a sufficient condition for the design of a dynamic output feedback controller which makes the closed loop system finite-time stable. Such sufficient condition is given in terms of an LMI optimization problem; this gives the opportunity of fitting the finite-time control problem in the general framework of the LMI approach to the multi-objective synthesis. In this context an example illustrates the design of a controller which guarantees, at the same time, finite-time stability together with some pole placement requirements.     

一类扩展结构大系统的分散有限时间鲁棒关联镇定

研究一类扩展结构大系统分散有限时间鲁棒关联镇定问题. 扩展结构大系统是在原结构系统上增加新子系统而构成的, 在原系统分散控制律确定不变的情况下, 设计新加入子系统的鲁棒分散控制律, 使扩展后的系统仍能保持有限时间关联稳定. 利用LMI 方法推导此类系统基于状态反馈和输出反馈的分散有限时间关联镇定的充分条件, 并给出扩展子系统的相应控制器的设计方法. 最后通过仿真实验表明了所提出方法的可行性和有效性.

     

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

This paper considers the preview tracking control problem of polytopic uncertain discrete‐time systems with a time‐varying delay subject to a previewable reference signal. First, a model transformation is employed and a discrete‐time system with a time‐invariant delay and an external disturbance is obtained. The difference operator method can be extended to derive an augmented error system that includes future information on the reference signal. Then, a previewable reference signal is fully utilized through reformulation of the output equation while considering the output feedback. Based on the small gain theorem, a static output feedback controller with preview actions is designed such that the output can asymptotically track the reference signal. Finally, numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the paper.