鲁棒镇定区间系统族的一个充分条件

讨论了区间系统族的鲁棒镇定问题,给出存在控制器鲁棒镇定区间系统族的一个充分条 件,并且当这个条件成立时,得到了鲁棒镇定区间系统族的控制器的参数化公式.     

混合不确定性系统的鲁棒镇定及性能设计

采用双回路控制方法讨论具有混合不确定性系统的鲁棒镇定及性能设计问题，其内环控制器可改善对象特性，从而使整个双回路闭环系统具有鲁棒稳定性．     

菱形对象族的顶点镇定结果

本文研究了菱形对象族的鲁棒镇定问题。当控制器取为分子，分母为仅有奇次项的或仅有偶次荐的多项式的真有理分式时，证明了该控制器鲁棒镇定菱形对象族的充分必要条件为该控制器同时镇定三十二个顶点对象。当上述控制器的分子，分母限于正负交错系数的仅有奇次项的或仅有偶次项的多项式时，该控制器鲁棒镇定菱形对象族所需同时镇定的顶点对象最多为十六个，所进结果与对象族的阶次无关。     

多线性凸多面体对象族的鲁棒镇定

研究了由多个不确定对象串联所构成的多线性凸多面体对象族的鲁棒镇定问题,在对控 制器的结构进行某些假设的条件下,给出了控制器鲁棒镇定对象族的充分必要条件是它同时镇定 所有的顶点对象.     

菱形对象族的鲁棒镇定*

本文研究了菱形对象族的鲁棒镇定问题，证明了控制器鲁棒镇定菱形对象族的充分必要条件是它同同时镇定六十四条棱边对象，在此基础上，利用凸方向的概念讨论了控制器分子、分母的选择，并给出了菱形对象族的顶点镇空结果。     

无穷范数意义下的可镇定半径问题

利用棱边定理给出了计算参数未知的区间对象族能镇定半径的解析式. 对于参数区间确定且标称对象相同的区间对象族, 通过本文方法计算出的可镇定半径, 只要参数变化范围小于能镇定半径时, 即可确保给定区间对象族能镇定. 最后, 通过一个计算例子说明了本文的方法.     

约束不确定非线性系统的鲁棒优化镇定

针对状态和输入约束不确定非线性仿射系统,提出一种鲁棒镇定的优化控制器设计方法.基于弱鲁棒控制Lyapunov函数概念,构造一个参数可调控制器.再利用LaSalle定理和逆优化理论,验证该控制器的鲁棒镇定性和逆最优性.进一步,采用滚动优化原理在线计算控制器的可调参数,实现闭环系统的鲁棒优化镇定.最后对一个开环不稳定振荡器系统进行鲁棒优化镇定,其结果验证了文中方法的有效性.     

同时镇定及鲁棒控制器存在条件

在保证闭环系统稳定的前提下，将被控对象看成控制器，控制器看成被控对象。从集合的角度研究了镇定区间对象族的控制器存在条件和设计方法，利用值集的概念和Youla参数化结果给出了镇定区间对象族控制器存在的充分条件．在强约束条件下，得到了控制器存在的充要条件．最后给出了鲁棒镇定控制器的设计方法．     

线性时滞系统滞后反馈鲁棒镇定

本文研究时不变线性时滞系统的鲁棒镇定问题。通过建立时滞系统的一个渐近稳定性定理，对摄动矩阵满足匹配条件和不满足匹配条件的情况分别给出了完全鲁棒镇定控制器的设计方法与鲁棒镇定控制器的存在性充分条件和设计方法；文中尤其提出了非滞后线性系统的一种简单的滞后反馈镇定方案。文末用例子示例了本文的设计方法。     

Schur-Cohn多项式的鲁棒稳定半径

研究离散线性时不变系统的特征多项式的鲁棒稳定性, 给出用求多项式最小值的方法来估计Schur_Cohn多项式的鲁棒稳定半径, 在一定条件下估计为最优估计. 最后, 给出若干算例.     

可镇定性可以是参数鲁棒镇定问题的可解性充分条件

This paper deals with the robust stabilization problem for an interval plant family P(s, δ). It is shown that an interval plant may be robustly stabilized by a single controller C(s) if every member plant of P(s, δ) is stabilizable.     

有限字长数字控制器的实稳定半径最优实现

主要讨论了有限字长(FWL)数字控制器的一种最优实现问题,考察了一个典型的采样反馈系统,将实有理稳定半径测度应用到有限字长数字控制器的实现问题中,对实稳定半径测度进行优化,并由此得到控制器的最优状态变换矩阵和最优结构及最小字长.数值算例验证了优化的结果是有效的,优化后较小字长的控制器就可以使系统取得较大的稳定半径.     

Robust stability with structured real parameter perturbations

This paper considers the problem of robust stabilization of a linear time-invariant system subject to variations of a real parameter vector. For a given controller the radius of the largest stability hypersphere in this parameter space is calculated. This radius is a measure of the stability margin of the closed-loop system. The results developed are applicable to all systems where the closed-loop characteristic polynomial coefficients are linear functions of the parameters of interest. In particular, this always occurs for single-input (multioutput) or single-output (multiinput) systems where the transfer function coefficients are linear or affine functions of the parameters. Many problems with transfer function coefficients which are nonlinear functions of physical parameters can be cast into this mathematical framework by suitable weighting and redefinition of functions of physical parameters as new parameters. The largest stability hyperellipsoid for the case of weighted perturbations and a stability polytope in parameter space are also determined. Based on these calculations a design procedure is proposed to robustify a given stabilizing controller. This algorithm iteratively enlarges the stability hypersphere or hyperellipsoid in parameter space and can be used to design a controller Io stabilize a plant subject to given ranges of parameter excursions. These results are illustrated by an example.     

Data-Driven Global Robust Optimal Output Regulation of Uncertain Partially Linear Systems

In this paper, a data-driven control approach is developed by reinforcement learning (RL) to solve the global robust optimal output regulation problem (GROORP) of partially linear systems with both static uncertainties and nonlinear dynamic uncertainties. By developing a proper feedforward controller, the GROORP is converted into a global robust optimal stabilization problem. A robust optimal feedback controller is designed which is able to stabilize the system in the presence of dynamic uncertainties. The closed-loop system is ensured to be input-to-output stable regarding the static uncertainty as the external input. This robust optimal controller is numerically approximated via RL. Nonlinear small-gain theory is applied to show the input-to-output stability for the closed-loop system and thus solves the original GROORP. Simulation results validates the efficacy of the proposed methodology.      

一种自适应鲁棒控制方法及其闭环稳定性分析

研究了含有未建模动态的慢时变系统的自适应镇定问题.考虑的对象具有非最小相 位、含未建模动态和大范围时变参数等不良特性,且存在未知但有界外部扰动.这类对象很难 用时不变鲁棒控制器或传统自适应控制器进行镇定.利用l1优化设计结合参数估计的投影算 法,提出了一种自适应鲁棒控制策略.基于l1优化设计的连续性和投影算法的收敛性,证明了 这种控制策略能够持续适应慢时变对象并且保持闭环系统一致稳定性.鲁棒性分析表明这种 控制策略具有良好的鲁棒镇定性.     

Robust stability analysis of control systems with interval plants

This paper considers the robust stability problem of control systems with interval plants. Under the condition that the controller C(s) stabilizes the nominal plant P0(s) which is the centre of the interval plant, the stability radius of the closed-loop system is characterized in terms of the eigenvalues of some frequency-independent Hurwitz-like matrices.     

混合不确定性系统的鲁棒镇定及性能设计

采用双回路控制方法讨论具有混合不确定性系统的鲁棒镇定及性能设计问题,其内环控 制器可改善对象特性,从而使整个双回路闭环系统具有鲁棒稳定性.     

An almost necessary and sufficient condition for robust stability of closed-loop systems with disturbance observer

The disturbance observer (DOB)-based controller has been widely employed in industrial applications due to its powerful ability to reject disturbances and compensate plant uncertainties. In spite of various successful applications, no necessary and sufficient condition for robust stability of the closed loop systems with the DOB has been reported in the literature. In this paper, we present an almost necessary and sufficient condition for robust stability when the Q-filter has a sufficiently small time constant. The proposed condition indicates that robust stabilization can be achieved against arbitrarily large (but bounded) uncertain parameters, provided that an outer-loop controller stabilizes the nominal system, and uncertain plant is of minimum phase.     

Stabilization via Nonsmooth, Nonconvex Optimization

Nonsmooth variational analysis and related computational methods are powerful tools that can be effectively applied to identify local minimizers of nonconvex optimization problems arising in fixed-order controller design. We support this claim by applying nonsmooth analysis and methods to a challenging "Belgian chocolate" stabilization problem posed in 1994: find a stable, minimum phase, rational controller that stabilizes a specified second-order plant. Although easily stated, this particular problem remained unsolved until 2002, when a solution was found using an eleventh-order controller. Our computational methods find a stabilizing third-order controller without difficulty, suggesting explicit formulas for the controller and for the closed loop system, which has only one pole with multiplicity 5. Furthermore, our analytical techniques prove that this controller is locally optimal in the sense that there is no nearby controller with the same order for which the closed loop system has all its poles further left in the complex plane. Although the focus of the paper is stabilization, once a stabilizing controller is obtained, the same computational techniques can be used to optimize various measures of the closed loop system, including its complex stability radius or H_infin performance