Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.

Book Announcement of L. Celentano, Robust Tracking Controllers Design with Generic References for Continuous and Discrete Uncertain Linear SISO Systems, LAP LAMBERT Academic Publishing, 2012

In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, without zeros, and with measurable state. The controller guarantees that the control system is Type 1 and has the desired constant gain and poles or that the control system tracks, with a specified maximum error and with a specified maximum time constant, a generic reference with bounded derivative (variation in the discrete-time case), also in the presence of a generic disturbance with bounded derivative (variation). In addition, it is considered the case in which the reference is known a priori. The utility and the efficiency of the proposed methods are illustrated with attractive and significant examples of motion control and temperature control. This book is useful for the design of control systems, especially for manufacturing systems, that are versatile, fast, precise and robust.

Peak-to-Peak Gain Minimization for Uncertain Linear Discrete Systems： A Matrix Inequality Approach

为不明确的线性分离系统的一个班的 peak-to-peak 获得最小化的一条矩阵不平等途径被学习。我们最小化 * 是导致的 L 标准上的最好的上面的界限的 -norm, 由与逃避不了的椭圆体围住可达到的集合获得了，而不是直接最小化导致的 L 标准。基于这个想法，柔韧的 peak-to-peak 获得最小化的问题和控制器合成被归结为解决一套矩阵不平等的可行性问题。一个数字例子被用来表明介绍方法的可行性和有效性。

Iterative learning based fault diagnosis for discrete linear uncertain systems

In order to detect and estimate faults in discrete lin-ear time-varying uncertain systems, the discrete iterative learning strategy is applied in fault diagnosis, and a novel fault detection and estimation algorithm is proposed. And the threshold limited technology is adopted in the proposed algorithm. Within the chosen optimal time region, residual signals are used in the proposed algorithm to correct the introduced virtual faults with iterative learning rules, making the virtual faults close to these occurred in practical systems. And the same method is repeated in the rest optimal time regions, thereby reaching the aim of fault diagnosis. The proposed algorithm not only completes fault detection and estimation for discrete linear time-varying uncertain systems, but also improves the reliability of fault detection and decreases the false alarm rate. The final simulation results verify the validity of the proposed algorithm.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

Robust stability analysis of uncertain discrete-time systems with state delay

The sufficient conditions of stability for uncertain discrete-time systems with state delay have been proposed by some researchers in the past few years, yet these results may be conservative in application. The stability analysis of these systems is discussed, and the necessary and sufficient condition of stability is derived by method other than constructing Lyapunov function and solving Riccati inequality. The root locations of system characteristic polynomial, which is obtained by augmentation approach and Laplace expansion, determine the stability of uncertain discrete-time systems with state delay, the system is stable if and only if all roots lie within the unit circle. In order to analyze robust stability of system characteristic polynomial effectively, Kharitonov theorem and edge theorem are applied. Example shows the practicability of these methods.

Robust Optimal H∞ Control for Uncertain 2-D Discrete State-Delayed Systems Described by the General Model

This paper investigates the problem of robust optimal H∞ control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H∞ state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

Delay-Dependent Robust H∞ Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

This paper considers the problem of delay-dependent robust optimal H∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H∞ noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H∞ controller which minimizes the H∞ noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

Stabilizing Hybrid Stochastic Interval Systems by Feedback Controls

The problem of stabilizing a hybrid stochastic interval system is studied in this article. A hybrid interval system with suitable controls will become stable in the sense of mean-square exponential stability. State-feedback controls are designed based on the discrete-time state observations. Controls are put both in the drift and diffusion parts of the system. Criteria are derived in terms of linear matrix inequalities( LMI) to get the controllers. Also one example is given to illustrate our techniques.

Robust Neural Control of Discrete Time Uncertain Nonlinear Systems Using Sliding Mode Backpropagation Training Algorithm

This work deals with robust inverse neural control strategy for a class of single-input single-output(SISO) discrete-time nonlinear system affected by parametric uncertainties. According to the control scheme, in the first step, a direct neural model(DNM)is used to learn the behavior of the system, then, an inverse neural model(INM) is synthesized using a specialized learning technique and cascaded to the uncertain system as a controller. In previous works, the neural models are trained classically by backpropagation(BP) algorithm. In this work, the sliding mode-backpropagation(SM-BP) algorithm, presenting some important properties such as robustness and speedy learning, is investigated. Moreover, four combinations using classical BP and SM-BP are tested to determine the best configuration for the robust control of uncertain nonlinear systems. Two simulation examples are treated to illustrate the effectiveness of the proposed control strategy.

Efficient robust supervisors for discrete event systems

This paper is a sequel to a previous publication by the same authors, in which an efficient modular solution to a robust supervisory control problem for discrete event systems modeled by finite automata with prefix-closed specification languages has been presented. This solution is based on a general recursive robust control scheme, which has been successfully applied to a number of problems. The additional contributions of the present paper are： （a） a slight generalization of the problem assumptions; （b） an alternative derivation of some of the results and an alternative formulation of the controller; （c） a detailed description of a very efficient on-line implementation algorithm; and （d） an illustrative practical example.

基于等价输入干扰的不确定离散时间系统预见重复控制

针对一类具有外部干扰的不确定线性离散系统,提出一种基于等价输入干扰(equi-valent input disturbance,EID)补偿的预见重复控制设计方法。首先,为了在提高系统跟踪精度的同时对外部干扰进行主动抑制,提出一种前向通道包含预见和重复控制器、反馈通道包含EID补偿的多自由度系统结构。然后,利用T阶差分算子,获得包含目标信号预见信息、重复控制器输出以及重构干扰的增广离散系统。于是,设计控制器的问题,变成了离散系统在二次性能指标下的稳定性问题。进一步,利用Lyapunov稳定性理论和线性矩阵不等式(linear matrix inequality,LMI)处理技巧,得到系统稳定性条件,进而获得控制器参数化方法。最后,数值仿真验证了所提方法的有效性。

一种控制输入约束下的不确定离散系统非脆弱保性能控制器设计

【目的】针对考虑扰动及摄动情况下的控制输入约束的不确定离散系统,提出了非脆弱保性能的控制方法。【方法】首先,以最小化目标函数为性能指标、控制输入饱和范围为约束条件,从而推导出约束状态下的非脆弱保性能控制律。其次,使用李雅普诺夫方程来构造非线性矩阵不等式。再次,结合Schur补定理和布谷鸟群智能优化算法对不等式进行求解,得到控制输入约束下的非脆弱保性能控制律的参数。最后,通过Quanser三自由度陀螺仪平台进行试验验证。【结果】试验结果表明,本研究所提出方法的稳态误差浮动不超过0.07、跟踪误差不超过0.15。【结论】该方法在面对扰动及摄动情况时具有更高的鲁棒性,对提升三自由度陀螺仪的稳定性及控制精度具有重要意义。

不确定情景下AGV系统调度算法的仿真平台

不确定情境下的完整自动引导车(automated guided vehicle,AGV)系统调度算法,除了要包含常见的任务指派策略和路径规划算法之外,还需要包含冲突应对策略。由于存在随机性,这样的调度算法难以从理论上分析其特性,相关研究也较少。基于离散事件仿真技术,设计并开发了一个AGV系统仿真平台,可以灵活地设置调度问题,并选择调度算法中的任务指派策略、路径规划算法和路径冲突应对策略进行仿真。该平台具有可视化的界面,可以直观地观察AGV的运行状态和调度算法的表现,也可以输出最终的仿真实验统计数据。实验表明:该平台可以准确有效地对不确定情景下的调度算法进行评估与比较。

离散广义系统具有完整性的鲁棒二次稳定

研究时不变不确定离散广义系统具有完整性的鲁棒二次稳定问题.首先,给出不确定离散广义系统鲁棒二次稳定的充要条件.其次,利用广义代数R iccati不等式,设计状态反馈使得不确定离散广义系统鲁棒二次稳定.进一步,给出状态反馈设计方法,使得不确定离散闭环广义系统在执行器正常以及部分出现故障情况下,都保持鲁棒二次稳定.即不确定广义系统具有完整性.同时,还讨论了所给的广义代数R iccati不等式的求解问题.最后给出数字例子来验证所给结果的有效性.

不确定离散时间系统的变结构控制设计

讨论了利用离散趋近律设计不确定离散时间系统的变结构控制问题 ,分析了离散趋近律系数造成系统颤振的原因 ,给出了改进的离散趋近律 ,并利用它设计了变结构控制律 ,对不确定部分建立灰色估计模型 ,估计出参数值 .仿真结果表明该方法是可行的 。

不确定离散变结构控制系统的趋近律方法

分析了不确定离散变结构控制系统的常用设计方法的优缺点,借助s型函数提出了一种改进的离散趋近律.应用该趋近律设计的变结构控制系统,其原点稳定性和系统平稳性都优于指数趋近律和变速趋近律,该设计方案保证了系统状态在趋近过程中能够保持某一趋近特性,加快了系统状态的趋近速度,同时降低了抖振,易于变结构控制设计.仿真结果验证了该设计方案的可行性和有效性.

时变不确定离散时滞系统的H_∞鲁棒控制

研究了一类线性不确定离散时滞系统的H∞ 鲁棒控制问题 ,其时变不确定项是范数有界的 ,但无需满足匹配条件 .基于线性矩阵不等式 (LMI)方法 ,得到了可H∞ 鲁棒镇定的一个充分条件 .通过求解一个特定的线性矩阵不等式 ,即可获得H∞ 状态反馈控制器 .

不确定离散广义系统的时滞相关非脆弱无源控制

针对不确定离散时滞广义系统,研究其时滞相关鲁棒严格无源、渐近稳定性以及相关的非脆弱控制问题.首先利用线性矩阵不等式(LMI)和自由权矩阵的概念,分析了离散广义系统时滞相关严格无源以及渐近稳定性的条件;然后讨论不确定离散广义系统的时滞相关鲁棒严格无源和渐近稳定性,并讨论具有加性非脆弱反馈控制设计使得闭环系统满足相应性能,同时给出控制器的构造方法;最后通过数值算例说明该方法的有效性.