一类线性离散时间大系统的预见重复控制

文章针对一类线性离散时间大系统提出一种预见重复控制方法.结合预见控制和重复控制的优势,构造带有预见补偿作用和学习能力的控制器,即预见重复控制器,实现对预见周期性目标值信号的跟踪.首先,通过状态增广技术和二维模型方法,构造包含可预见目标值信号的二维扩大误差系统;其次,针对扩大误差系统,分别考虑状态反馈和输出反馈,并基于Lyapunov函数方法及线性矩阵不等式(LMI)技巧给出预见重复控制器设计方法.最后,通过比较预见重复控制、重复控制和预见控制,表明文章结果的有效性.     

二维非稳态对流扩散边界控制问题的简化算法

针对二维非稳态对流扩散边界控制问题计算量大的问题,提出了基于降阶模型的最优实时控制方法.利用POD(the Proper Orthogonal Decomposition)和奇异值分解以及Galerkin投影方法得到了具有高精度离散形式的状态空间降阶模型.在所得的降阶状态空间模型中,利用离散时间线性二次调节器方法设计出了最优控制器.对流-扩散过程的控制模拟结果说明了所提方法的有效性和准确性.     

非线性网络控制系统的保性能控制

针对网络诱导时延小于一个采样周期的非线性网络控制系统,研究了系统的稳定性和保性能控制问题.对于T-S模糊模型描述的非线性被控对象,将时延的不确定性转化为系统参数的不确定性,从而将这一类非线性网络控制系统建模为具有参数不确定性的离散T-S模糊模型.基于建立的模型,提出了存在稳定保性能控制器的充分条件,并得出了相应的线性矩阵不等式(LMI)形式.最后通过对永磁同步电动机混沌系统进行控制和仿真研究,验证了所提出方法的有效性.     

线性不确定系统的鲁棒D型迭代学习控制

研究一类线性不确定系统的鲁棒D型迭代学习控制问题.首先针对一类线性标称控制对象,建立其迭代学习控制的二维模型;然后基于获得的二维模型,利用二维系统稳定性理论,获得系统在迭代初态与期望初态一致和不一致两种情形下的D型迭代学习控制律的存在条件和设计方法;进一步,将所得结果推广至控制对象包含不确定性的情形.所得结果以线性矩阵不等式(LMI)的形式给出,可以方便地利用Matlab中的LMI工具箱求解.最后,数值仿真实例验证了本文所提方法的有效性.     

分布时延网络控制系统的H_∞优化控制

研究了具有分布时延和扰动的网络控制系统H_∞优化控制问题.连续系统中的网络时延必须分开讨论.针对线性时不变被控对象,基于连续动态输出反馈控制器,建立了同时含有连续项和离散项的混合系统模型.利用Lyapunov-Krasovskii泛函,推导出系统可实现γ-次优H_∞镇定的充分条件.通过引入等式约束的方法将其转化为线性矩阵不等式,给出了系统H_∞次优控制器参数和扰动衰减度的求取方法,并将该系统H_∞最优控制问题转化为线性目标最小化问题.仿真算例说明了分析方法和结果是有效可行的.     

基于Delta算子离散化方法的永磁同步电机H_∞控制系统

在建立永磁同步电机(PMSM)Delta算子离散化模型的基础上,利用线性矩阵不等式(LMI)方法对PMSM的H_∞控制问题进行研究.以LMI形式给出了PMSM H_∞控制器参数存在的充分条件,通过求解LMI得出PMSM H_∞控制器参数.最后对PMSM H_∞控制系统的稳定性问题进行分析,并给出负载和给定转速发生变化时PMSM H_∞控制系统的速度响应曲线,结果表明,快速采样时基于Delta算子离散化方法所设计的H_∞控制器不但能保证PMSM闭环系统的稳定性,而且能较好的改善PMSM的跟随给定和抗干扰能力.     

离散重置系统的前向完备性和稳定性

提出一种离散时间重置控制系统的二维指标模型.与现有模型不同的是,二维指标模型可以描述重置的瞬时性.基于该模型,研究了离散重置系统的前向完备性,得到了关于前向完备性的充分必要条件.研究了单步重置次数的有界性,给出了界的估计.最后,得到了关于稳定性的充分条件.     

多输入离散T-S模糊双线性模型与模糊控制器设计

针对一类多输入离散非线性系统给出了基于模糊双线性T-S模型的参数化新模型,用并行分布补偿算法(PDC)设计模糊控制器,以线性矩阵不等式(LM I)的形式给出系统H∞全局稳定的充分条件,并通过求解一系列线性矩阵不等式(LM I)给出控制器增益的设计方法,最后,通过仿真例子验证这个方法的有效性和可行性。     

离散系统迭代学习型瞬时最优控制及作动器位置优化研究

以线性离散系统为研究对象,以瞬时最优化控制和智能算法中的迭代学习控制为基础,以系统响应期望值与实际值之差为反馈信号,以离散系统的二次型性能泛函为目标函数,提出了迭代学习型瞬时最优控制算法.该方法以瞬时最优化控制算法初始化控制信号,并采用迭代学习控制在线实时修正控制信号以提高主动控制的效果.针对迭代学习型瞬时最优化控制算法迭代的特性,采用范数方法给出了该算法收敛的充分条件.数值算例表明,迭代学习型瞬时最优控制算法较离散瞬时最优控制算法有较明显的优势.同时,基于改进遗传算法,对主动控制器位置优化进行了讨论.数值分析结果表明:部分楼层设置主动控制器且安装位置经过优化后,其控制效果可接近甚至优于全楼层设置主动控制器时的控制效果.     

Markov跳变系统滚动时域有限记忆控制

针对离散时间Markov跳变系统,提出滚动时域有限记忆控制的方法.在一段有限滤波时域上,利用系统输入与输出变量的线性组合构造一段有限控制时域上的输出反馈控制器.首先,不考虑跳变系统均方可镇定,基于最优控制的方法,获得以迭代计算形式给出的控制器,并使其在无偏条件下能优化二次型性能指标.其次,进一步考虑在成本衰减条件下确定终端加权矩阵,并以它作为边界条件计算得到最优控制律,调节系统均方稳定.为便于求解,成本衰减条件以线性矩阵不等式的形式给出.仿真实例验证了所提方法的可行性和有效性.     

不确定时滞系统的时滞相关非脆弱鲁棒[[H_infty]]控制

讨论了不确定时滞系统非脆弱控制器设计问题.利用Lyapunov-Krasovskii稳定性理论和最近建立的积分不等式方法,获得了不确定时滞系统在非脆弱控制器作用下不仅内部渐近稳定,而且具有给定的H∞扰动抑制水平γ的时滞相关条件.然后,针对控制器具有加法不确定性和乘法不确定性两种情况,分别给出了非脆弱控制器的设计方法,这一方法不需要调节参数,利用Matlab的LMI工具箱求解方便,数值仿真实例说明该方法的有效性.     

广义不确定周期时变系统的鲁棒非脆弱控制

研究了状态矩阵具有不确定性的广义周期时变系统的鲁棒非脆弱控制问题.利用线性矩阵不等式(LMI)方法,分别对控制器增益具有加法式摄动和乘法式摄动两种情形加以讨论,而非脆弱控制器的设计可以通过求解一组线性矩阵不等式得到.最后,数值例子说明了所给方法的有效性.     

Composite nonlinear feedback based discrete integral sliding mode controller for uncertain systems

In this paper, a discrete integral sliding mode (ISM) controller based on composite nonlinear feedback (CNF) method is proposed. The aim of the controller is to improve the transient performance of uncertain systems. The CNF based discrete ISM controller consists of a linear and a nonlinear term. The linear control law is used to decrease the damping ratio of the closed-loop system for yielding a quick transient response. The nonlinear feedback control law is used to increase the damping ratio with an aim to reduce the overshoot of the closed-loop system as it approaches the desired reference position. It is observed that the discrete CNF-ISM controller produces superior transient performance as compared to the discrete ISM controller. The closed-loop control system remains stable during the sliding condition. Simulation results demonstrate the effectiveness of the proposed controller.     

Non-fragile observer-based passive control for uncertain time delay systems subjected to input nonlinearity

The problem of non-fragile observer-based passive control for uncertain time delay systems subjected to input nonlinearity is investigated by using sliding mode control. A novel control law is established such that the sliding surface in the state-estimation space can be reached in a finite time and chattering reduction is obtained. A sufficient condition for passivity and asymptotic stability of the combined system is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantages of the proposed method.     

An online identification algorithm of unknown time-varying delay and internal multimodel control for discrete non-linear systems

In this paper, an online algorithm is proposed for the identification of unknown time-varying input delay in the case of discrete non-linear systems described by decoupled multimodel. This method relies on the minimization of a performance index based on the error between the real system and the partial internal models outputs. In addition, a decoupled internal multimodel control is proposed for the compensation of discrete non-linear systems with time-varying delay. This control scheme incorporates partial internal model controls. Each partial controller is associated to a specified operating zone of the non-linear system. The switching between these controllers is ensured by a supervisor that contains a set of local predictors. A simulation example is carried out to illustrate the significance of the proposed time-varying delay identification algorithm and the proposed internal multimodel control scheme.     

Stabilization of nonlinear networked systems with sensor random packet dropout and time-varying delay

In this paper, a nonlinear stochastic system model is proposed to describe the networked control systems (NCSs) with both random packet dropout and network-induced time-varying delay. Based on this more general nonlinear NCSs model, by choosing appropriate Lyapunov functional and employing new discrete Jensen type inequality, a sufficient condition is derived to establish the quantitative relation of maximum allowable delay upper bound, packet dropout rate and the nonlinear level to the exponential stability of the nonlinear NCSs. Design procedures for output feedback controller are also presented in terms of utilizing cone complementarities linearization algorithm or solving corresponding linear matrix inequalities (LMIs). Illustrative examples are provided to demonstrate the effectiveness of the proposed method.     

Model predictive control of nonlinear hybrid systems with discrete inputs employing a hybrid fuzzy model

The paper deals with model predictive control (MPC) of nonlinear hybrid systems with discrete inputs based on reachability analysis. In order to implement a MPC algorithm, a model of the process that we are dealing with is needed. In the paper, a hybrid fuzzy modelling approach is proposed. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for hybrid fuzzy modelling purposes is tackled. An efficient method of identification of the hybrid fuzzy model is also discussed.

An algorithm that is–due to its MPC nature–suitable for controlling a wide spectrum of systems (provided that they have discrete inputs only) is presented.

The benefits of the algorithm employing a hybrid fuzzy model are verified on a batch reactor example. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid–nonlinear–stiff systems such as the batch reactor.

Finally, a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model is carried out. It has been established that the latter approach clearly outperforms the approach where a linear model is used.     

Positive real control for 2-D discrete delayed systems via output feedback controllers

This paper considers the problem of positive real control for two-dimensional (2-D) discrete delayed systems in the Fornasini–Marchesini second local state-space model. Attention is focused on the design of dynamic output feedback controllers, which guarantee that the closed-loop system is asymptotically stable and the closed-loop transfer function is extended strictly positive real. We first present a sufficient condition for extended strictly positive realness of 2-D discrete delayed systems. Based on this, a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality (LMI). When the LMI is feasible, an explicit parametrization of a desired output feedback controller is presented. Finally, we provide a numerical example to demonstrate the application of the proposed method.     

Dynamic periodic event-triggered gain-scheduling control co-design for quasi-LPV systems

This paper investigates dynamic periodic event-triggered gain-scheduling control co-design for nonlinear systems subject to disturbances. The considered class of nonlinear systems is such that an equivalent polytopic quasi-LPV model is obtained. Based on the co-design approach, gain-scheduled control law and dynamic event-triggering mechanism (ETM) are jointly designed. The proposed co-design condition is formulated in terms of linear matrix inequality (LMI) conditions which are derived from the Bessel–Legendre inequality and the delay-dependent reciprocally convex combination lemma. As the state information is available to the gain-scheduled controller at specific instants determined by the ETM, it induces the asynchronous phenomenon between the parameters of the controller and the plant’s quasi-LPV model. To reduce the conservativeness induced by this asynchronous phenomenon, an LMI relaxation is proposed. Numerical examples illustrate the advantages of the proposed dynamic periodic event-triggered control co-design approach over its static counterpart.     

网络化马尔可夫跳变系统的鲁棒无源控制

针对基于网络的凸多面体不确定离散时间马尔可夫跳变系统,研究其鲁棒无源控制问题.在网络诱导时滞是时变且有界的情况下,基于李雅普诺夫稳定性理论,通过构造参数依赖的随机李雅普诺夫泛函和运用广义系统变换,提出了不依赖模态的无源控制器存在的时滞依赖充分条件.所设计的鲁棒无源控制器保证了相应的闭环系统是鲁棒随机稳定且具有指定耗散率.将鲁棒无源控制器设计问题转化为一组线性矩阵不等式的可解性问题.仿真算例证明了本文方法的有效性.