Robust Control Using Interval Analysis

The synthesis procedure of a control law that guarantees properties of robust stability with respect to structured parameter perturbations is proposed. The solution of the considered problem is based on the Razumikhin's method for functional differential equations generalized for parameter perturbation systems with time delay. The extension is obtained by using interval Lyapunov functions. The robust control law is represented through a solution of an interval matrix Riccati type equation.     

Robust Autonomous Robot Localization Using Interval Analysis

This paper deals with the determination of the position and orientation of a mobile robot from distance measurements provided by a belt of onboard ultrasonic sensors. The environment is assumed to be two-dimensional, and a map of its landmarks is available to the robot. In this context, classical localization methods have three main limitations. First, each data point provided by a sensor must be associated with a given landmark. This data-association step turns out to be extremely complex and time-consuming, and its results can usually not be guaranteed. The second limitation is that these methods are based on linearization, which makes them inherently local. The third limitation is their lack of robustness to outliers due, e.g., to sensor malfunctions or outdated maps. By contrast, the method proposed here, based on interval analysis, bypasses the data-association step, handles the problem as nonlinear and in a global way and is (extraordinarily) robust to outliers.Luc Jaulin: on leave from Laboratoire d'Ingénierie des Systèmes Automatisés, Université d'Angers, 2 bd Lavoisier, 49045 Angers, FranceLuc Jaulin: on leave from Laboratoire d'Ingénierie des Systèmes Automatisés, Université d'Angers, 2 bd Lavoisier, 49045 Angers, FranceLuc Jaulin: on leave from Laboratoire d'Ingénierie des Systèmes Automatisés, Université d'Angers, 2 bd Lavoisier, 49045 Angers, France     

Design Of Robust Pid Controllers

In this paper, a new method is proposed to design the robust PID controllers for uncertain linear time‐invariant systems. We describe a simple and programming procedure for designing PID controllers by applying Kharitonov's theorem and LMI method. Such a controller enables the resulting control system to achieve robust stability as well as asymptotic tracking.     

单一与非单一鲁棒控制器的设计

针对普通二次Lyapunov函数方法判定T-S模糊系统稳定性存在的保守性和难度,利用T-S系统的模糊前提规则和隶属度函数分别构造分段二次Lyapunov函数和模糊Lyapunov函数,且通过将模糊Lyapunov函数引入到分段二次Lyapunov函数所得到的分段模糊区域中定义了分段模糊Lyapunov函数;研究一类T-S模糊系统的鲁棒控制问题,以线性矩阵不等式的形式给出了单一与非单一鲁棒控制器的参数化设计方法。仿真结果表明,非线性系统在非单一鲁棒控制器作用下能够获得比单一鲁棒控制器更好的控制性能。     

Design of Robust Output Controllers via Frequency Conditions

Frequency conditions determining the parameters of dynamic output controllers for different classes of uncertain systems, such as nonlinear Lur'e systems, systems with parameters switched by an unknown law, and systems with unknown bounded parameters, are formulated.     

Wiener滤波问题的一种Diophantine方程解

用时域上的现代时间序列分析方法,基于ARMA新息模型和白噪声估值器,提出Wiener滤波问题的一种Diophantine方程解。它可统一处理平稳或非平稳ARMA信号的最优滤波、平滑和预报问题。仿真例子说明了其有效性。     

用VHDL设计十六路彩灯控制器

VHDL设计技术是引起数字系统设计方式发生突破性变革的技术。本文论述了使用VHDL设计十六路彩灯控制器的过程。VHDL为设计提供了更大的灵活性,使程序具有更高的通用性。     

Design of Robust Linear Controllers under Parametric Uncertainty of the Object Model

Consideration was given to the design of continuous and discrete robust controllers for multidimensional systems with parametric uncertainty. Algorithms to calculate the weight matrices at the coordinates of the output vector and at the equivalent external perturbations in the dynamic model of the object for which the controllers that are optimal in the quadratic or H criterion guarantee stability of the closed-loop system within the given domain of parametric uncertainty were proposed, and examples were presented.     

离散区间系统的鲁棒稳定性分析

本文主要研究了离散区间系统的稳定性问题,以线性矩阵不等式的形式给出了离散区间系统鲁棒稳定性的充分条件,最后通过仿真验证了该方法是行之有效的。     

An Iterative Method of the Structural-Parametric Design of Robust Systems with State Controllers

An iterative method for designing a robust control system with state controllers is proposed that includes a transformation of the plant structure to improve its controllability by correcting the singular values of the controllability Gramian and the subsequent synthesis of the basic controller for the corrected plant using modal control. This approach allows us to design systems satisfying the robust stability condition for the given intervals of variation of the plant parameters.     

Nonconvex Polygon Interval Arithmetic as a Tool for the Analysis and Design of Robust Control Systems

This paper describes Nonconvex Polygon Interval Arithmetic (NPIA) and its implementation. NPIA is the arithmetic defined on the set of all polygons in the complex plane, and it is very useful to compute estimates of value sets of transfer functions including uncertain physical parameters in a reasonable computing time. If the transfer function can be written in such a way that each uncertain parameter appears at most once, then the estimate obtained is included in an neighborhood of the region enclosed by the outer boundary of the value set.     

区间离散广义系统的鲁棒稳定性分析

讨论一类区间离散广义系统的鲁棒稳定性问题。在给出区间离散广义系统的等价描述之后,基于线性矩阵不等式,得到了问题的充要条件,数值例子说明了该方法的正确性。     

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.     

分数阶区间系统的鲁棒稳定性分析

由于实际的物理系统常会存在各种不确定结构,这些不确定结构给系统的稳定性分析带来了困难和一定的影响,因此对这类带有不确定结构的分数阶系统控制问题的研究,具有广泛的实际应用意义。本文主要针对带有区间不确定性的分数阶控制系统,分析了该系统的鲁棒稳定性问题,首先将区间矩阵用分式线性变换(LFT)表示,然后基于分析得出了此类系统鲁棒稳定的充分必要条件。并给出两个数值算例阐释该方法,仿真结果表明了该方法的有效性。     

离散区间系统鲁棒容错控制器的设计

讨论了离散线性系统的鲁棒容错控制问题.针对离散线性系统,当系统矩阵和控制矩阵存在参数区间摄动时,通过Lyapunov稳定性理论分析了系统同时存在传感器失效情况下的鲁棒稳定问题,给出了系统鲁棒稳定的一个充分条件,并在此基础上给出离散区间系统鲁棒容错控制器的设计方法.最后用数值算例解释了该算法的有效性.     

Type-II型模糊控制器的结构分析与设计

全面研究了Type-II型模糊控制器的解析结构,推导出了单输入单输出和双输入单输出Type-II型模糊控制器的插值解析表达式,在一定程度上揭示了其本质特征。在此基础上,提出了Type-II型模糊控制器的一般设计步骤、优化方法和一种快速精确的控制算法。     

不确定时滞系统基于观测器的鲁棒控制器设计

研究了不确定线性时滞系统的状态观测器和基于观测器的鲁棒控制器设计问题，其中不确定性是时变的，通过构造增广系统，利用线性矩阵不等式方法，获得了该不确定系统存在状态观测器和基于观测器的鲁棒控制器的充分条件，同时给出了相应的状态观测器和基于观测器的鲁棒控制器，所给示例说明了本文方法的设计步骤和有效性。     

基于信息量的模糊控制器的设计

文章根据信息量的不同,介绍基于Lyapunov函数和基于极点配置局部稳定的T-S模型的两类模糊控制器设计方法。并且在MATLAB环境中进行了仿真和实验。实验结果表明：Lyapunov函数法具有良好的抗干扰能力,鲁棒性强,可控范围小;极点配置法响应速度快、可控范围大。并且这两种方法具有互补性。