力矩受限的机器人吸引域估计方法

针对力矩受限的机器人组合非线性反馈控制的局部稳定区域描述问题,研究了吸引域的估计方法.利用不变集属性和椭球性质,定义两种不同意义的最大椭球不变集来逼近吸引域,分别采用设置初始状态法和参考形状集法求解.通过带有约束的优化问题描述,所有条件均能转化为线性矩阵不等式条件,易于求解.由于采用优化技术,能够减小吸引域估计的保守性.数值算例验证了所提方法的有效性.

     

基于N步不变集的时滞切换系统的饱和控制

构造离散时滞切换系统的不变集,提出基于N步不变集的切换控制器设计方法,估计执行器饱和非线性的吸引域范围。首先,考虑时滞的影响,选取依赖于时滞的Lyapunov函数,构造时滞切换系统的不变集,并将其表达为若干个椭球集的凸组合,椭球集的个数与时滞常数相关。其次,在系统的前N个采样时刻,分别施加不同的饱和约束,求解得到一组椭球集,椭球集的个数与常数N相关,而每一步计算得到的椭球集均为时滞切换系统的不变集。再将N个不变集用一组凸包系数拟合,即可获取较大的吸引域估计。最后,在满足平均驻留时间约束的条件下设计切换律,并设计状态反馈控制器,保证闭环系统渐近稳定。控制器的求解转化为线性矩阵不等式的可行性问题。仿真结果验证了所提方法的可行性和有效性。     

奇异线性系统在执行器饱和受限下不变集条件的改进

本文考虑饱和线性反馈下奇异线性系统扩大吸引域估计的问题.根据每个输入是否饱和,将输入空间分成若干子区域.在每个子区域内部,系统模型中没有显示的部分状态的时间导数可被显式表达.利用含有全部系统状态的二次Lyapunov函数,建立一组双线性矩阵不等式形式的改进的不变集条件.该组条件下,二次Lyapunov函数的水平集可诱导出一个吸引域估计.为得到最大的吸引域估计,构建了以这些双线性矩阵不等式为约束条件的优化问题,并为其求解给出了迭代算法.仿真结果表明本文得到的吸引域估计明显大于现有结果.     

输入非线性广义预测控制系统的吸引域分析与设计

对输入非线性包括输入饱和与Hammerstein非线性的系统,采用两步法广义预测控 制(TSGPC)策略.首先不考虑输入非线性,采用线性GPC求解期望的中间变量,然后采用 解方程的方法处理Hammerstein非线性并用解饱和方法满足饱和约束.将TSGPC转化为状 态空间描述,研究该控制策略的吸引域问题.将吸引域的求解化为迭代求解的优化问题,给 出了求解算法和满足给定吸引域要求的控制器的调整方法.通过仿真验证了理论结果.     

基于吸引域的总体极小化问题的神经网络求解

神经网络求解优化问题具有非常强大的实时计算功用,因此近年来受到了密切的关注.这里考察了求解无约束总体极小化问题的神经网络方法,提出了一种新的网络求解模型.从基于吸引域分析方法为出发点证明了所给网络平稳点集合的全局吸引性.分析了网络的电路实现,并估计了各个平稳点的吸引域.这些理论分析与估计是构造所提神经网络模型的依据,同时也是网络可靠运行的基础.此外,数值模拟试验也充分揭示了这个网络模型在实际运行中都能够很好地求解总体极小化问题,是一个十分有效的神经网络系统.这里的结果表明:这里提出的网络模型无论从理论上还是实际运行中都能够可靠且稳定地求解总体极值问题,基于吸引域构造神经网络的方法是一种很有潜力的神经网络求解优化问题的研究方向.     

基于MIT规则的自适应扩展集员估计方法

用于非线性椭球估计的自适应扩展集员(Adaptive extended set-membership filter, AESMF)算法在实际应用中存在着过程噪声设定椭球与真实噪声椭球失配的问题, 导致滤波器的估计出现偏差甚至发散. 本文提出了一种基于MIT规则过程噪声椭球最优化的自适应扩展集员估计算法(MIT-AESMF), 用于解决非线性系统时变状态和参数的联合估计和定界中过程噪声无法精确建模问题的新算法. 本算法通过MIT优化规则,在线计算使一步预测偏差包络椭球最小化的过程噪声包络椭球, 以此保证滤波器健康指标满足有效条件; 最后, 采用地面移动机器人状态和动力学参数联合估计验证了所提出方法的有效性.     

多面体上彷射系统可达性问题研究

研究n维多面体上自治仿射系统的可达性问题. 目的在于得到多面体上最大正不变集和每个极大面的反向可达集(吸引域). 研究最大稳定不变仿射子空间, 并给出不变集和吸引域的性质, 最后通过分割算法确定两者的边界.     

一种估计奇异摄动饱和系统稳定域的方法

针对奇异摄动饱和系统, 提出了一种估计其稳定域的降阶方法. 结合饱和函数的特殊性质, 证明了此类系统的稳定域可分解为伴随系统的不变集与一个足够大球体的笛卡尔积. 将原系统稳定域估计问题转化为低阶伴随系统稳定域的估计问题, 利用线性矩阵不等式(Linear matrix inequality, LMI)优化方法估计伴随系统的稳定域以减少保守性. 本方法不仅可以克服奇异摄动饱和系统的奇异性, 还可以一定程度克服系统的``维数灾'等问题.     

执行器饱和不确定NCS 非脆弱鲁棒容错控制

针对存在时变时延和丢包的不确定网络化控制系统(NCS), 同时考虑执行器饱和、控制器参数摄动以及非线性扰动等约束, 研究执行器发生结构性失效故障时系统的鲁棒容错多约束控制问题. 基于时滞依赖Lyapunov 方法和容错吸引域定义, 采用状态反馈控制策略推证出了闭环故障不确定网络化控制系统稳定的少保守性不变集充分条件, 并给出了非脆弱鲁棒容错控制器的设计方法以及最大容错吸引域的估计. 仿真算例验证了所述方法的可行性和有效性.

     

一种改进的鲁棒约束预测控制器的综合设计方法

针对多包描述的不确定系统,提出一种新的鲁棒约束预测控制器.高线设计多包系统worst-case情况下性能最优的不变集,在线求解多包系统无穷时域性能指标的rain-max优化问题.设计方法采用了时变的终端约束集,扩大了初始可行域,并能获得较优的控制性能.仿真结果验证了该方法的有效性.     

The Ellipsoidal Invariant Set of Fractional Order Systems Subject to Actuator Saturation: The Convex Combination Form

The domain of attraction of a class of fractional order systems subject to saturating actuators is investigated in this paper. We show the domain of attraction is the convex hull of a set of ellipsoids. In this paper, the Lyapunov direct approach and fractional order inequality are applied to estimating the domain of attraction for fractional order systems subject to actuator saturation. We demonstrate that the convex hull of ellipsoids can be made invariant for saturating actuators if each ellipsoid with a bounded control of the saturating actuators is invariant. The estimation on the contractively invariant ellipsoid and construction of the continuous feedback law are derived in terms of linear matrix inequalities (LMIs). Two numerical examples illustrate the effectiveness of the developed method.      

On estimation of attraction domain for port-controlled Hamiltonian systems subject to actuator saturation

This paper investigates the estimation of domain of attraction for nonlinear port-controlled Hamiltonian (PCH) systems with actuator saturation (AS).Several conditions are established under which an el...     

受约束时滞系统的抗饱和补偿器增益设计

Systems that are subject to both time-delay in state and input saturation are considered.We synthesize the anti-windup gain to enlarge the estimation of domain of attraction while guaran-teeing the stability of the closed-loop system. An ellipsoid and a polyhedral set are used to bound the state of the system, which make a new sector condition valid. Other than an iterative algorithm, a direct designing algorithm is derived to compute the anti-windup compensator gain, which reduces the conservatism greatly. We analyze the delay-independent and delay-dependent cases, respectively. Finally, an optimization algorithm in the form of LMIs is constructed to compute the compensator gain which maximizes the estimation of domain of attraction. Numerical examples are presented to demonstrate the effectiveness of our approach.     

An analysis and design method for discrete-time linear systems under nested saturation

This paper considers a discrete-time linear system under nested saturation. Nested saturation arises, for example, in systems with actuators subject to both magnitude and rate saturation. A condition is derived in terms of a set of auxiliary feedback gains for determining if a given ellipsoid is contractively invariant. Moreover, this condition is shown to be equivalent to linear matrix inequalities (LMIs) in the actual and auxiliary feedback gains. As a result, the estimation of the domain of attraction for a given set of feedback gains is then formulated as an optimization problem with LMI constraints. By viewing the feedback gains as extra free parameters, the optimization problem can be used for controller design.     

模型参数失配有界下的扩展集员估计方法

在非线性模型参数失配下,直接采用滤波算法很难获到理想的估计状态.本文基于扩展集员估计方法,在状态估计中引入参数的不确定信息,提出一种参数失配有界下的状态估计方法.该方法应用区间或集合运算的法则,计算由参数失配引起的偏差范围,并将其用椭球集外包.在状态估计的预测步,通过该偏差椭球集与先验椭球区间的并运算,得到预测椭球区间;在状态估计的更新步,利用观测椭球集对预测椭球区间进行更新,从而得到后验椭球集合以及状态估计值.最后,在数值仿真和发酵模型中的仿真应用验证了算法的有效性.     

An analysis and design method for linear systems under nested saturation

This paper considers a linear system under nested saturation. Nested saturation arises, for example, when the actuator is subject to magnitude and rate saturation simultaneously. A condition is derived in terms of a set of auxiliary feedback gains for determining if a given ellipsoid is contractively invariant. Moreover, this condition is shown to be equivalent to linear matrix inequalities (LMIs) in the actual and auxiliary feedback gains. As a result, the estimation of the domain of attraction for a given set of feedback gains can be formulated as an optimization problem with LMI constraints. By viewing the feedback gains as extra free parameters, the optimization problem can be used for controller design.     

Analysis and design for discrete-time linear systems subject to actuator saturation

We present a method to estimate the domain of attraction for a discrete-time linear system under a saturated linear feedback. A simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant. Moreover, the condition can be expressed as linear matrix inequalities (LMIs) in terms of all the varying parameters and hence can easily be used for controller synthesis. The following surprising result is revealed for systems with single input: suppose that an ellipsoid is made invariant with a linear feedback, then it is invariant under the saturated linear feedback if and only if there exists a saturated (nonlinear) feedback which makes the ellipsoid invariant. Finally, the set invariance condition is extended to determine invariant sets for systems with persistent disturbances. LMI based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements.     

Estimate of Domain of Attraction for a Class of Port‐Controlled Hamiltonian Systems Subject to Both Actuator Saturation and Disturbances

This paper investigates the estimate of domain of attraction for a class of nonlinear port‐controlled Hamiltonian (PCH) systems subject to both actuator saturation and disturbances. Firstly, two conditions are established to determine whether an ellipsoid is contractively invariant for the systems only with actuator saturation, with which the biggest ellipsoid contained in the domain of attraction can be found. Secondly, the obtained conditions are extended to estimate the domain of attraction of the systems subject to both actuator saturation and disturbances. Study of illustrative example shows the effectiveness of the method proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stability and stabilization of discrete-time periodic linear systems with actuator saturation

This paper is concerned with the problems of stability and stabilization for discrete-time periodic linear systems subject to input saturation. Both local results and global results are obtained. For local stability and stabilization, the so-called periodic invariant set is used to estimate the domain of attraction. The conditions for periodic invariance of an ellipsoid can be expressed as linear matrix inequalities (LMIs) which can be used for both enlarging the domain of attraction with a given controller and synthesizing controllers. The periodic enhancement technique is introduced to reduce the conservatism in the methods. As a by-product, less conservative results for controller analysis and design for discrete-time time-invariant systems with input saturation are obtained. For global stability, by utilizing the special properties of the saturation function, a saturation dependent periodic Lyapunov function is constructed to derive sufficient conditions for guaranteeing the global stability of the system. The corresponding conditions are expressed in the form of LMIs and can be efficiently solved. Several numerical and practical examples are given to illustrate the theoretical results proposed in the paper.