一类不确定性系统的鲁棒正实性分析与综合

考虑一类具有多项式型不确定性系统的鲁棒正实性分析和综合问题。这类不确定模型是区间摄动和范数有界摄动系统的自然推广。给出了一个系统具有鲁棒扩展严格正实性 (ESPR)的充分条件 ,利用该条件可估计出使系统保持 ESPR的最大参数摄动范围。在 ESPR分析的基础上 ,进一步给出了ESPR控制器的存在条件和控制器的构造方法。通过凸优化算法 ,得到了所提出方法意义下具有最大摄动界的 ESPR控制器设计方法。     

鲁棒严格正实镇定的顶点结果

本文主要研究了区间系统的鲁棒严格正实镇定问题。文中首先给出了系统严格正实镇定的充分条件。然后分析了该条件的可计算性并对一类区间分母系统获得了采用一阶控制器时鲁棒严格正实镇定的顶点结果，使得控制器设计大为简化。     

连续和离散系统的鲁棒严格正实性*

本文提出了一种统一的鲁棒严格正实性判定准则，既适用于连续系统，又适用于离散系统，在此准则的基础上，形成了鲁棒严格正实滤波器和补偿器的设计方法，当考虑的系统是线性参数摄动系统或由若干个独立线性参数摄动系统串联成的，则本文给出的是端点结果。     

严格正实线性多变量系统的鲁棒性分析及其输出反馈控制

讨论一类线性不确定系统的鲁棒严格正实分析和控制问题，其中各不确定参数矩阵具有线性分式形式，分析了这类系统对所有容许不确定性严格正实的条件，并综合了使闭环内稳且严格正实的动态输出反馈控制器，通过适当地构造增广系统，将这类问题转化为确定系统的严格正实分析和设计，并按增广系统给出了这类不确定系统鲁棒严格正实的充分必要条件以及动态输出反馈鲁棒严格正实控制器的存在条件。     

Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis

In this paper, a robust fractional‐order PID (FOPID) controller design method for fractional‐order delay systems is proposed based on positive stability region (PSR) analysis. Firstly, the PSR is presented to improve the existing stability region (SR) in D‐decomposition method. Then, the optimal fractional orders λ and μ of FOPID controller are achieved at the biggest three‐dimensional PSR, which means the best robustness. Given the optimal λ and μ, the other FOPID controller parameters k_p, k_i, k_d can be solved under the control specifications, including gain crossover frequency, phase margin, and an extended flat phase constraint. In addition, the steps of the proposed robust FOPID controller design process are listed at length, and an example is given to illustrate the corresponding steps. At last, the control performances of the obtained robust FOPID controller are compared with some other controllers (PID and FOPI). The simulation results illustrate the superior robustness as well as the transient performance of the proposed control algorithm.     

一阶系统预测PID控制器鲁棒稳定性分析

针对基于DCS预测PID的控制系统,利用Kharitonov定理和边缘理论分析其在参数不确定情况下输入/输出鲁棒稳定性。具体对一阶加纯滞后对象给出了系统保持稳定的最大过程参数区间。仿真结果表明,当过程参数偏离标称值时,该方法能使系统保持很好的鲁棒稳定性。     

离散广义系统的鲁棒严格正实控制

研究确定的以及具有范数有界不确定性的离散广义系统的严格正实分析和控制问题,首先给出了确定离散广义系统状态反馈扩展严格正实控制器的存在条件和设计方法;然后利用线性矩阵不等式分析了不确定离散广义系统广义二次稳定且扩展严格正实的条件,讨论了状态反馈使闭环系统广义二次稳定且扩展严格正实问题,给出了状态反馈鲁棒扩展严格正实控制器的综合方法;最后通过数值算例说明了所提出方法的有效性．     

Robust control design of a class of nonlinear systems in polynomial lower-triangular form

This paper investigates the problem of global robust stabilization for a wide class of nonlinear systems, called polynomial lower-triangular form (pLTF), which expands LTF to a more general case. The aim is explicitly constructing the smooth controller for the class of systems with static uncertainties, by adding and modifying a power integrator in a recursive manner. The pLTF relaxes the restrictions on the structure of the normal LTF and enlarges the family of systems that are stabilizable. Examples are also provided to show the practical usage of this class of systems and the effectiveness of the design method. Recommended by Editorial Board member Hyungbo Shim under the direction of Editor Jae Weon Choi. Bing Wang received the B.S. degree from the Huazhong University of Science and Technology, and the Ph.D. degree from the University of Science and Technology of China, in 1998 and 2006, respectively. He is currently working in College of Electrical Engineering, Hohai University. His research interests include robust control, nonlinear control and power systems. Haibo Ji received the B.S. and Ph.D. degrees in Mechanical Engineering from ZheJiang University and Beijing University in 1984 and 1990 respectively. He is currently a Professor in the Dept. of Automation, USTC. His research interests include nonlinear control and adaptive control. Jin Zhu received the B.S. and Ph.D. degrees in Control Science and Engineering from University of Science & Technology of Chinain 2001 and 2006 respectively. He is currently a Post-doc in Han-Yang University, Korea. His research interests include Markovian jump systems and nonlinear control.     

Robust output regulation and the preservation of polynomial closed‐loop stability

In this paper, we study the robust output regulation problem for distributed parameter systems with infinite‐dimensional exosystems. The main purpose of this paper is to demonstrate the several advantages of using a controller that achieves polynomial closed‐loop stability, instead of a one stabilizing the closed‐loop system strongly. In particular, the most serious unresolved issue related to strongly stabilizing controllers is that they do not possess any known robustness properties. In this paper, we apply recent results on the robustness of polynomial stability of semigroups to show that, on the other hand, many controllers achieving polynomial closed‐loop stability are robust with respect to large and easily identifiable classes of perturbations to the parameters of the plant. We construct an observer based feedback controller that stabilizes the closed‐loop system polynomially and solves the robust output regulation problem. Subsequently, we derive concrete conditions for finite rank perturbations of the plant's parameters to preserve the closed‐loop stability and the output regulation property. The theoretical results are illustrated with an example where we consider the problem of robust output tracking for a one‐dimensional heat equation.Copyright © 2013 John Wiley & Sons, Ltd.     

复杂摄动系统的鲁棒稳定性判定方法

本文讨论了由几个区间多项式族相乘和相加后形成的多项式族,根据其值域的几何性质,提出了这类复杂摄动多项式族鲁棒稳定性的判定方法.     

基于LM I 的广义系统正实反馈控制

建立连续情形广义系统新的正实引理，通过对线性矩阵不等式(LMI)的求解和系统的等价变换，给出了正实状态反馈控制的充分必要条件，构造了保持系统稳定性的正实控制器设计方法，数值实例表明，该求解控制器的方法简单方便，具有实际意义。     

基于混沌多项式的指令鲁棒优化及在飞行控制中的应用

本文提出一种新的方法对随机系统进行运动预测和控制指令设计,该方法可以充分利用已知信息设计控制指令以提高闭环随机系统的鲁棒性.首先采用混沌多项式对随机信息进行数学表述,并利用Galerkin投影法将随机变量的混沌多项式引入常微分方程中.然后,将随机变量的均值和方差考虑至优化问题的成本函数中,并利用伪谱法对控制指令进行鲁棒优化.最后,将该方法应用于飞行器的动力学预测以及控制指令设计.仿真结果表明,该方法能够预测飞行器飞行过程中不确定性的演化,其精度与蒙特卡罗方法相当,并且计算效率更高.此外,获得的控制指令对存在不确定参数或初始条件的随机系统具有强鲁棒性.     

Robust stability analysis of systems with real parametric uncertainty: A global optimization approach

This paper presents an optimization framework for the robustness analysis of linear and nonlinear systems with real parameter uncertainty. For linear systems, a nonlinear programming formulation for the exact calculation of the stability margin is presented. The potential of decomposition-based global optimization methods for the solution of this nonconvex problem is discussed. Next the concept of the stability margin is extended to a class of nonlinear systems. A nonlinear stability margin and a uniqueness margin are defined to address the effect of parametric uncertainty on the stability of a particular steady state, as well as on the number of steady states of the system. This analysis allows for the derivation of necessary and sufficient conditions for robust stability and robust uniqueness of the steady state of the system in the presence of parametric uncertainty.     

Robust stability of positive switched systems with dwell time

This paper studies robust stability of positive switched systems (PSSs) with polytopic uncertainties in both discrete-time and continuous-time contexts. By using multiple linear copositive Lyapunov functions, a sufficient condition for stability of PSSs with dwell time is addressed. Being different from time-invariant multiple linear copositive Lyapunov functions, the Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards. Then, robust stability of PSSs with polytopic uncertainties is solved. All conditions are solvable via linear programming. Finally, illustrative examples are given to demonstrate the validity of the proposed results.     

系数空间中多项式的鲁棒稳定性和有理函数的严格正实不变性*

本文在多项式的系数空间中讨论离散时间意义下多项式的鲁棒稳定性和有理函数的严格正实不变性,证明了对于系数空间中的某种超矩形,其顶点多项式的稳定性就保证了全族无穷多个多项式的稳定性;对于有理函数的严格正实性,本文也得到了类似的结论。     

On Hurwitz stability for families of polynomials

The robustness of a linear system in the view of parametric variations requires a stability analysis of a family of polynomials. If the parameters vary in a compact set $A$, then obtaining necessary and sufficient conditions to determine stability of the family ${\mathfrak{F}}_A$ is one of the most important tasks in the field of robust control. Three interesting classes of families arise when $A$ is a diamond, a box or a ball of dimension $n+1$. These families will be denoted by ${\mathfrak{F}}_{D_n}$, ${\mathfrak{F}}_{B_n}$, and ${\mathfrak{F}}_{S_n}$, respectively. In this article, a study is presented to contribute to the understanding of Hurwitz stability of families of polynomials ${\mathfrak{F}}_A$. As a result of this study and the use of classical results found in the literature, it is shown the existence of an extremal polynomial $f({\alpha }^{\ast },x)$ whose stability determines the stability of the entire family ${\mathfrak{F}}_A$. In this case $f({\alpha }^{\ast },x)$ comes from minimizing determinants and in some cases $f({\alpha }^{\ast },x)$ coincides with a Kharitonov's polynomial. Thus another extremal property of Kharitonov's polynomials has been found. To illustrate our approach, it is applied to families such as ${\mathfrak{F}}_{D_n}$, ${\mathfrak{F}}_{B_n}$, and ${\mathfrak{F}}_{S_n}$ with $n\le 5$. The study is also used to obtain the maximum robustness of the parameters of a polynomial. To exemplify the proposed results, first, a family ${\mathfrak{F}}_{D_n}$ is taken from the literature to compare and corroborate the effectiveness and the advantage of our perspective. Followed by two examples where the maximum robustness of the parameters of polynomials of degree 3 and 4 are obtained. Lastly, a family ${\mathfrak{F}}_{B_5}$ is proposed whose extreme polynomial is not necessarily a Kharitonov's polynomial. Finally, a family ${\mathfrak{F}}_{S_3}$ is used to exemplify that if the boundary of $A$ is given by a polynomial equation in several variables, the number of candidates to be an extremal polynomial is finite.     

A new decentralised controller design method for a class of strongly interconnected systems

In this paper, two interconnected structures are first discussed, under which some closed-loop subsystems must be unstable to make the whole interconnected system stable, which can be viewed as a kind of strongly interconnected systems. Then, comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown. A new approach for the design of decentralised controllers is presented by determining the Lyapunov function structure previously, which allows the existence of unstable subsystems. By fully utilising the orthogonal space information of input matrix, some new understandings are presented for the construction of Lyapunov matrix. This new method can deal with decentralised state feedback, static output feedback and dynamic output feedback controllers in a unified framework. Furthermore, in order to reduce the design conservativeness and deal with robustness, a new robust decentralised controller design method is given by combining with the parameter-dependent Lyapunov function method. Some basic rules are provided for the choice of initial variables in Lyapunov matrix or new introduced slack matrices. As byproducts, some linear matrix inequality based sufficient conditions are established for centralised static output feedback stabilisation. Effects of unstable subsystems in nonlinear Lur'e systems are further discussed. The corresponding decentralised controller design method is presented for absolute stability. The examples illustrate that the new method is significantly effective.     

Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1‐gain and L∞‐gain characterization

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are employed here for robustness and performance analysis using L₁‐gain and L_∞‐gain. Robust stability analysis is performed using integral linear constraints for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's theorem. Several examples are provided for illustration. Copyright © 2012 John Wiley & Sons, Ltd.     

一类互联电力系统的鲁棒联结稳定性分析

研究一类互联电力系统在不确定结构扰动下的鲁棒联结稳定问题．基于系统中互联矩阵的不确定性给出了鲁棒联结稳定的定义,利用向量Lyapunov函数方法及范数、特征值的性质推导了此类系统鲁棒联结稳定的两个充分条件．对系统在不确定结构扰动下联结稳定的鲁棒程度进行分析,得到了不确定参数的鲁棒界．两区域互联电力系统的仿真实例说明了所推导条件的有效性．