Pole assignment for uncertain systems in a specified disk by output feedback

In this paper the problem of pole assignment in a disk by output feedback for continuous-or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given.     

Disk pole location for uncertain systems through convex optimization

In this paper, a necessary and sufficient condition for disk pole location for uncertain continuous or discrete time systems subject to norm-bounded uncertainty is derived. This condition being convex, the control law design is made through convex optimization. The approach adopted follows the quadratic stabilizability philosophy in the problem of pole placement.     

Robust pole assignment in systems subject to structured perturbations

The problem of robust pole assignment by feedback in a linear, multivariable, time-invariant system which is subject to structured perturbations is investigated. A measure of robustness, or sensitivity, of the poles to a given class of perturbations is derived, and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure.     

On pole structure assignment in linear systems

The problem of pole structure assignment (PSA) by state feedback in implicit, linear and uncontrollable systems is discussed in the article. It is shown that the problem is solvable if the system is regularisable. Then necessary and sufficient conditions for characteristic polynomial assignment are established. In the case of PSA (invariant polynomials assignment) just necessary conditions have been obtained. But it turns out that these conditions are also sufficient in some special cases. This happens, for example, when the system does not possess any non-proper controllability indexes. A possible application of the achieved results to modelling a constrained movement of a robot arm is outlined, too.     

Dominant pole and eigenstructure assignment for positive systems with state feedback

In this paper, the dominant pole assignment problem, the dominant eigenstructure assignment problem and the robust dominant pole assignment problem for linear time-invariant positive systems with state feedback are considered. The dominant pole assignment problem is formulated as a linear programming problem, and the dominant eigenstructure problem is formulated as a quasiconvex optimisation problem with linear constraints. The robust dominant pole assignment problem is formulated as a non-convex optimisation problem with non-linear constraints which is solved using particle swarm optimisation (PSO) with an efficient scheme which employs the dominant eigenstructure assignment technique to accelerate the convergence of the PSO procedure. Each of the three problems can be further constrained by requiring that the controller has a pre-specified structure, or the gain matrix have both elementwise upper and lower bounds. These constraints can be incorporated into the proposed scheme without increasing the complexity of the algorithms. Both the continuous-time case and the discrete-time case are treated in the paper.     

输入多采样率数字控制系统的同时极点配置

在利用提升(lifting)技术所构造出来的多采样率数字控制系统的线性时不变状态空间模型的基础上, 讨论l个被控对象通过输入多采样率数字控制系统的同时极点配置问题. 分别引入了解决这一问题的状态空间方法和多项式矩阵插值方法. 通过适当的变换, 将同时极点配置问题归结为一系列线性方程组的求解问题. 指出, 当系统的输入采样率满足一定条件时, 可以利用输入多采样率的输出静态反馈控制系统, 实现对l个被控对象的同时极点配置.     

A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems

Pole assignment is a basic design method for synthesis of feedback control systems. In this paper, a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems. The proposed approach is shown to be capable of synthesizing linear output feedback control systems via on-line robust pole assignment. Convergence of the gradient flow can be guaranteed. Moreover, with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed-loop control system based on the gradient flow is globally exponentially stable. These desired properties make it possible to apply the proposed approach to slowly time-varying linear control systems. Simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach.     

具有域极点配置的混合H2/H∞滤波

解决了具有域极点配置的连续时不变系统的混合H2/H∞滤波问题.通过采用线性矩阵不等式(LMI)方法描述域稳定性限制、H2和H∞优化,以建立求解这个问题的总框架.这个问题的可解性的充分必要条件由一组LMI给出.最后用一个数字例子来说明所给出的设计方法.     

基于极点配置的平整机张力解耦控制

分析了平整机产品质量存在的问题 ;提出了基于极点配置的解耦控制策略. 理论分析、计算机仿真和工业实验都表明该控制方法能实现对平整机前张力、后张力和工作辊速度的解耦控制, 降低了它们之间的相互耦合程度, 改善了系统的控制效果, 有利于提高带材产品的质量.     

离散不确定系统预估+ 步长修正变结构控制

在现有文献的基础上，给出一种预估＋步长修正的离散变结构控制律设计方法，该方法可用于离散时间不确定系统变结构控制，有效地抑制切换函数的发散振荡，克服现有方法中条件限制过程的缺点，仿真结果表明，该方法具有收敛性好，抖振小，鲁棒性强的优点。     

圆形区域内鲁棒极点配置优化

本文基于和声搜索算法将精确极点配置的思想推广到圆形区域极点配置,通过对圆域内极点全局优化的方法,实现圆域内鲁棒极点配置问题.首先,基于几何原理描述极点在圆形区域内的位置信息,确定了在圆形区域内动态选择极点的规则,可以保证算法在圆形区域内动态选取极点.然后,对圆形区域内的极点,基于精确鲁棒极点配置的思想,利用和声搜索算法优化摄动或不确定性的谱范数上界,从而得到一组允许闭环系统具有更大摄动或不确定性的极点及相应的状态反馈控制器.最后,通过实例进行仿真,仿真结果表明本文采用和声搜索算法全局优化动态选择极点方法得到的闭环系统具有更好的鲁棒性.     

区域极点配置问题的研究方法

对区域极点配置的现有研究成果进行综述.将区域极点配置的基本方法归结为代数Riccati方程(ARE)方法和线性矩阵不等式(LMI)方法.列出了基于区域极点配置方法的主要研究成果,包括最优控制、鲁棒性、H2性能、H∞性能等方面.最后给出了几点研究展望.     

具有域极点配置的混合H2 /H∞ 滤波

解决了具有域极点配置的连续时不变系统的混合H₂ /H_∞ 滤波问题. 通过采用线性矩阵不等式 (LMI)方法描述域稳定性限制、H₂ 和H_∞ 优化, 以建立求解这个问题的总框架. 这个问题的可解性的充分必要条件由一组LMI给出. 最后用一个数字例子来说明所给出的设计方法.     

一类不确定离散时间系统的鲁棒故障诊断滤波器优化设计方法

研究线性不确定离散时间系统的鲁棒故障诊断滤波器设计问题。基于新提出的性能指标函数，将不确定离散时间系统的故障诊断漶波器设计问题归结为肌优化问题，并通过选择适当的后滤波器和观测器增益矩阵，得到未知输入和模型不确定性鲁棒性的最优解。     

Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay

This paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete-time systems with state delay. The system under consideration involves state time delay and time-varying norm-bounded parameter uncertainties appearing in all the matrices of the state-space model. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities, respectively. A robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities. Two examples are presented to demonstrate the effectiveness of the proposed approach.     

Augmented gradient flows for on-line robust pole assignment via state and output feedback

This paper is concerned with robust pole assignment in synthesis of linear control systems via state and output feedbacks. First, both the pole assignment and robustness requirements are appropriately formulated as two optimization problems. Then, gradient flow models are developed for the on-line computation of feedback gain matrices that result in robust pole assignment by solving these two optimization problems. A technique is introduced to facilitate the real-time matrix inverse involved for realizing the gradient flow models. The resulting augmented gradient flows have desired convergence properties. Simulation results are included to show the effectiveness of the proposed approach.     

On pole assignment of linear systems by gain output feedback

In this paper, the Geometric Approach is used to derive in a straightforward way a sufficient condition for pole assignability by gain output feedback. This result leads to a pole assignment procedure which reduces to solving a system of min (n - m, n - p) polynomial equations where n is the number of states, m the number of inputs, p the number of outputs. In the case where m + p > n, this system clearly appears to be linear. The degrees of freedom related to the pole assignment problem are expressed in terms of (right or left) eigenvectors.     

Linear adaptive control for nonstationary uncertain systems under bounded noise

A discrete-time nonstationary linear control system is considered to be given by the algebraic difference equation in the state space. The control system is subject to a bounded additive noise. Uncertain parameters of the system take their values on the given polytopes which evolve in time. The objective is to generate a linear feedback, which provides the minimization of a given performance criterion in adaptive way. In general, the control problem is reduced to the convex programming one of an insignificant computational complexity. Therewith, the control problem can be solved analytically in the case of interval set-valued parameter estimates.