执行器饱和的线性连续系统的镇定

针对控制系统中广泛存在饱和问题,主要研究执行器饱和线性连续系统的镇定问题并进行吸引域估计。首先根据Finsler’s引理和Lyapunov函数方法研究系统稳定的充分条件,得到执行器饱和控制系统稳定的新判据。其次,在稳定条件下,应用凸组合方法和新引入的自由权矩阵使得系统吸引域估计具有更小的保守性,将所得非线性矩阵不等式转化为线性矩阵不等式,给出求解最大吸引域的优化方法和状态反馈控制器的设计方案。最后通过仿真算例验证结果的有效性和可行性。     

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.

     

二阶饱和线性系统的线性最优容错吸引域

考虑执行器故障影响,研究了二阶饱和线性系统的吸引域估计问题.通过适当定义容错吸引域,并采用椭圆逼近,使得系统的吸域域具有容错能力.为了保证容错吸引域的收敛性能,通过状态反馈将闭环系统极点配置在圆形极点区域内.基于参数空间,给出了圆形极点区域对应的反馈增益向量空间的不等式表示.在反馈增益向量窄间和执行器幅值的约束下,基于...     

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.     

基于LMI的小时滞饱和系统稳定域估计方法

基于Pade近似变换,将小时滞饱和系统的稳定域估计转化为估计奇异摄动饱和系统的稳定域问题.证明了此奇异摄动饱和系统的稳定域具有可解耦性,并在此基础上建立LMI优化模型并提出小时滞饱和系统稳定域估计的降阶方法.算例仿真验证了方法的正确性和有效性.     

带有饱和执行器的T-S离散模糊系统的LQ模糊控制

研究了带有饱和执行器的Takagi-SugenoT-S离散模糊系统的LQ模糊控制问题,利用Lyapunov稳定理论、PDC(平行分配补偿)技术以及线性矩阵不等式方法,得到了闭环模糊系统的渐近稳定的充分条件,给出了闭环系统的LQ模糊控制律的设计方法和吸引域的一个估计,并建立了闭环系统的LQ性能函数上界的计算公式.进一步,针对两类优化问题,即:LQ性能最小化问题和吸引域最大化问题,给出了相应的带有线性矩阵不等式约束的计算方法.最后,一个仿真例子说明了所给方法的有效性.     

基于系统输出的嵌套饱和系统抗饱和补偿器设计

针对嵌套输入饱和系统的吸引域扩大问题,本文提出了一种基于系统输出的抗饱和补偿器激发策略,将被控系统输出信号经性能补偿器馈入到抗饱和补偿器激发环节中,形成蕴含系统实时性能信息的抗饱和激发新机制,克服了传统抗饱和激发机制无法直接反映系统性能的缺点.基于上述抗饱和控制新框架,本文建立了抗饱和补偿器及性能补偿器存在的充分条件,并依此构建了优化问题求解最优补偿器增益以实现扩大闭环系统吸引域的目的.仿真结果表明本文方法的有效性.     

大规模离散线性系统的分散饱和反馈镇定(英文)

考虑了具有执行器饱和的大规模离散时间线性系统分散控制器的设计.首先进行了在执行器幅值饱和的情形下的研究,然后延伸到执行器具有多层饱和的情况,例如,幅值和速率同时存在饱和或通过多层神经元网络近似的执行器非线性.在这2种情况下,给出了闭环系统在分散状态反馈律的作用下,椭球收敛不变性的条件.基于这些条件,可取得大吸引域的分散状态反馈控制律的设计可以归结为具有双线性矩阵不等式(BMI)约束的优化问题.对这些双线性约束优化问题提出了数值算法.数值算例显示了所提出的设计方法的有效性.     

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.     

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。     

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ’large’ as possible. An example is provided to demonstrate the effectiveness of the new method.     

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.     

Analysis and design of discrete-time linear systems with nested actuator saturations

This paper is concerned with the analysis and design of discrete-time linear systems subject to nested saturation functions. By utilizing a new compact convex hull representation of the saturation nonlinearity, a linear matrix inequalities (LMIs) based condition is obtained for testing the local and global stability of the considered nonlinear system. The estimation of the domain of attraction and the design of feedback gains such that the estimation of the domain of attraction for the resulting closed-loop system is maximized are then converted into some LMIs based optimization problems. Compared with the existing results on the same problems, the proposed solutions are less conservative as more slack variables are introduced into the conditions. A couple of numerical examples are worked out to validate the effectiveness of the proposed approach.     

Conjugate Lyapunov functions for saturated linear systems

Based on a recent duality theory for linear differential inclusions (LDIs), the condition for stability of an LDI in terms of one Lyapunov function can be easily derived from that in terms of its conjugate function. This paper uses a particular pair of conjugate functions, the convex hull of quadratics and the maximum of quadratics, for the purpose of estimating the domain of attraction for systems with saturation nonlinearities. To this end, the nonlinear system is locally transformed into a parametertized LDI system with an effective approach which enables optimization on the parameter of the LDI along with the optimization of the Lyapunov functions. The optimization problems are derived for both the convex hull and the max functions, and the domain of attraction is estimated with both the convex hull of ellipsoids and the intersection of ellipsoids. A numerical example demonstrates the effectiveness of this paper's methods.     

Analysis and design of delta operator systems with nested actuator saturation

In this paper, the problem of estimating the domain of attraction is considered for delta operator systems subject to nested actuator saturation. A set invariance condition is established for the delta operator system with nested actuator saturation in terms of auxiliary feedback matrices. Based on the set invariance condition, an optimisation approach is proposed to estimate the domain of attraction for the delta operator system. Thereby, the partial results of nested actuator saturation for both continuous-time systems and discrete-time systems are extended to delta operator system framework. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.     

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     

Fault-tolerant control of delta operator systems with actuator saturation and effectiveness loss

This paper studies the problem of robust fault-tolerant control against the actuator effectiveness loss for delta operator systems with actuator saturation. Ellipsoids are used to estimate the domain of attraction for the delta operator systems with actuator saturation and effectiveness loss. Some invariance set conditions used for enlarging the domain of attraction are expressed by linear matrix inequalities. Discussions on system performance optimisation are presented in this paper, including reduction on computational complexity, expansion of the domain of attraction and disturbance rejection. Two numerical examples are given to illustrate the effectiveness of the developed techniques.     

Stability analysis and antiwindup design of uncertain discrete-time switched linear systems subject to actuator saturation

This paper investigates the stability analysis and antiwindup design problem for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the switched Lyapunov function approach.Supposing that a set of linear dynamic output controllers have been designed to stabilize the switched system without considering its input saturation,we design antiwindup compensation gains in order to enlarge the domain of attraction of the closed-loop system in the presence of saturation.Then,in terms of a sector condition,the antiwindup compensation gains which aim to maximize the estimation of domain of attraction of the closed-loop system are presented by solving a convex optimization problem with linear matrix inequality(LMI)constraints.A numerical example is given to demonstrate the effectiveness of the proposed design method.     

Control of periodic sampling systems subject to actuator saturation

In this paper, the control problem of linear systems with periodic sampling period subject to actuator saturation is considered via delta operator approach. Using periodic Lyapunov function, sufficient conditions of local stabilization for periodic sampling systems are given. By solving an optimization problem, we derive the periodic feedback control laws and the estimate of the domain of attraction. As the saturation function sat(·) belongs to the sector [0,1], sufficient conditions are derived by constructing saturation‐dependent Lyapunov functions to ensure that the periodic sampling system is globally asymptotically stable. A numerical example is given to illustrate the theoretical results proposed in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability analysis for continuous-time systems with actuator saturation

The aim of this paper is to study the determination of the stability regions for continuous-time systems subject to actuator saturation. Using an affine saturation-dependent Lyapunov function, a new method is proposed to obtain the estimation of the domain of attraction of the closed-loop system. A family of linear matrix inequalities （LMIs） that provides sufficient conditions for the existence of this type of Lyapunov function are presented. The results obtained in this paper can reduce the conservativeness compared with the existing ones. Numerical examples are given to illustrate the effectiveness of the proposed results.