双重不确定分数阶混沌系统的鲁棒自适应同步控制算法研究

针对一类含有未知参数且受外部扰动的双重不确定分数阶混沌系统的同步控制问题,提出一种易于实现的鲁棒自适应同步控制算法。基于分数阶Lyapunov稳定性定理和自适应控制策略,给出使同步误差系统鲁棒渐进稳定的自适应同步控制器设计方法。该控制器在实现混沌系统同步控制的同时,可以获得对未知参数的精确估计。以一类含绝对值项的分数阶混沌系统为例,通过MATLAB数值仿真验证该算法的有效性和可行性。     

基于主动滑模控制的一类不确定混沌系统的同步

讨论了一类不确定混沌系统的同步问题。基于主动控制思想,提出了一种新的主动滑模控制策略,使得从任意初始条件出发的不确定混沌系统在有限时间内趋近滑模面;通过一种新颖的虚拟反馈控制,得到了设计鲁棒滑模面的一个充分条件,较好地实现了响应系统与驱动系统的完全同步,确保了不确定混沌系统同步的鲁棒稳定性。该控制器适用于一般的混沌系统。以Lü混沌系统为例进行了仿真验证,仿真结果表明,该控制方法可以实现较快的混沌同步,且同步的鲁棒稳定性良好。     

一种参数优化的非线性离散系统鲁棒迭代学习控制方法

针对带有扰动的一类离散非线性系统的鲁棒迭代学习控制问题, 设计一种基于参数优化的迭代学习控制算法. 该算法能够保证在有初始状态误差和状态、输出扰动的情况下使闭环系统具有鲁棒BIBO 稳定性, 系统输出能够单调收敛于给定输出轨迹的邻域内; 在没有初始状态误差和扰动的情况下能够以零稳态误差跟踪给定输出轨迹. 最后通过仿真分析验证了所提出算法的有效性.

     

轧辊偏心的H∞输出反馈鲁棒重复控制

针对轧辊偏心问题,用线性矩阵不等式(LMI)方法设计了用于轧辊偏心补偿控制的H∞输出反馈鲁棒重复控制器,首先引入动态输出反馈来保证闭环系统的鲁棒稳定性,把重复控制器设计问题转化为H∞动态反馈控制器的设计问题,采用变量替换法将非线性矩阵不等式转化为线性矩阵不等式并对其求解进而得到控制器参数.另外在采用上述控制器保证系统鲁棒稳定性的同时,通过在重复控制器中引入一个前向系数进一步改善和提高系统的动态性能与稳态控制精度.理论证明与仿真研究表明当系统对象参数存在摄动时,这种控制器仍能有效地补偿轧辊偏心对产品质量的影响.     

采用鲁棒滑模观测器实现一类混沌系统的同步

提出一种鲁棒滑模观测器，并应用于一类混沌系统的同步，该鲁棒滑模观测器通过滑模与相应的控制策略来实现，可调整观测器跟踪系统状态的收敛速度，实现两个混沌系统的同步，将所提出的鲁棒滑模状态观测器用于一类存在参数摄动和／或干扰的混沌系统的同步具有鲁棒性，该鲁棒滑模状态观测器不仅能实现低维的混沌系统的同步，而且能实现超混沌系统的同步，以Chua’s电路和超混沌Roessler系统为例给出了设计过程和仿真实验，其结果验证了所提出方法的有效性。     

异结构混沌系统同步及其在保密通信中的应用*

根据主动控制思想和Lyapunov稳定性定理,构造主动控制器使得两个异结构的混沌系统在短时间内实现同步,并证明了混沌同步的鲁棒稳定性;利用MATLAB的Simulink技术进行数字仿真,将同步的异结构混沌系统应用到混沌掩盖和混沌参数调制保密通信中。仿真结果表明,异结构混沌系统能够实现稳定的同步,且在混沌掩盖和混沌参数调制保密通信中,有用信号均能有效地在接收端恢复出来。     

参数摄动混杂离散系统的鲁棒稳定性

采用线性矩阵不等式(LMI)方法研究离散事件状态转移条件为状态依赖的参数摄动线性混杂离散系统的鲁棒稳定性问题, 提出此类系统全局鲁棒渐近稳定性判定定理, 基于分段Lyapunov函数给出了一般混杂离散系统在Lyapunov意义下局部稳定的判定定理, 该定理可将线性混杂离散系统的稳定性问题转化为LMI问题, 在此基础上提出了参数摄动线性混杂离散系统在Lyapunov意义下局部鲁棒稳定的充分条件.     

不确定关联大系统分散鲁棒H∞输出反馈控制器设计

针对一类状态矩阵和控制矩阵存在参数不确定性关联大系统,研究其分散鲁棒H∞输出反馈控制问题。基于有界实引理将其鲁棒分散H∞动态输出反馈控制器的解归结为一个非线性矩阵不等式（NLMI）,采用同伦迭代算法求解该控制器,使大系统鲁棒稳定,并且满足给定的H∞性能指标。     

Delta 算子系统动态输出反馈 D-稳定鲁棒协方差控制

研究Delta 算子描述的线性不确定系统基于动态输出反馈的D- 稳定鲁棒协方差控制问题 .设计动态输出反馈控制器,使 Delta 算子不确定系统鲁棒D- 稳定,且稳态输出协方差矩阵具有给定上界. 利用线性矩阵不等式(LMI)方法,给出D- 稳定鲁棒协方差控制器存在的充分条件. 在此基础上,提出相应控制器的设计算法. 数值算例表明了该设计方法的可行性.

     

Constrained robust model predictive control via parameter-dependent dynamic output feedback

This paper considers output feedback robust model predictive control for the quasi-linear parameter varying (quasi-LPV) system with bounded disturbance. The so-called quasi-LPV means that the varying parameters of the linear system are known at the current time, but unknown in the future. The control law is parameterized as a parameter-dependent dynamic output feedback, and the closed-loop stability is specified by the notion of quadratic boundedness. An iterative algorithm is proposed for the on-line synthesis of the control law via convex optimization. A numerical example is given to illustrate the effectiveness of the controller.     

连续时间多胞线性变参数系统变增益H∞/H2输出反馈控制

针对一类同时具有参数不确定性和外界干扰的非线性系统,提出了一种连续时间多胞线性变参数(LPV)系统变增益H_∞/H_2输出反馈控制方法.首先,对连续时间多胞LPV系统的变增益混合目标(H_∞/H_2指标和区域极点约束)输出反馈控制器综合方法进行了数学描述;其次,引入新的结构化松弛矩阵变量和参数依赖Lyapunov函数,将满足期望性能的混合目标鲁棒动态输出反馈控制问题转化为线性矩阵不等式框架内的有限维凸优化问题,进一步降低了所设计LPV控制器的保守性.最后,以四分之一车辆模型主动悬架系统为研究对象进行仿真,仿真结果验证了本文控制器的有效性.     

不确定线性系统混合H2/H∞鲁棒输出反馈控制

解决了在系统状态空间模型的状态与输出矩阵中含有范数有界 参数不确定线性系统的混合Ｈ２／Ｈ∞鲁棒输出反馈控制问题,所推导的满阶控制器对于所有呆容许的参数不确定都能满足给定的Ｈ∞干扰衰减水平,且为最坏情形Ｈ２代价函数提供了一个最优的上界,所得的结果需要求解一个含有尺度参数的修正代数Ｒｉｃｃａｔｉ方程以及三个含有尺度参数的交叉耦合非线性方程,而且也给出了一个求解这些含有尺度参数非线性方程的数值算法。     

离散LPV重复过程的l2-l∞ 动态输出反馈控制

探究离散线性参数变化(LPV) 重复过程的l₂-l_∞ 动态输出反馈控制问题. LPV 重复过程是一类复杂的时变2D 系统. 对于整个参数变化空间, 传统方法是基于二次稳定框架设计过程的控制器, 具有较大的保守性. 这里利用参数依赖Lyapunov 函数, 设计离散LPV 重复过程的参数依赖鲁棒l₂-l_∞  动态输出反馈控制器, 可确保闭环离散LPV 重复过程沿通道渐近稳定, 且具有一定的l₂-l_∞  扰动抑制水平. 最后, 仿真结果验证了所提出方法的有效性.

     

Robust fault diagnosis for non-Gaussian stochastic systems based on the rational square-root approximation model

The task of robust fault detection and diagnosis of stochastic distribution control （SDC） systems with uncertainties is to use the measured input and the system output PDFs to still obtain possible faults information of the system. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper, a robust nonlinear adaptive observer-based fault diagnosis algorithm is presented to diagnose the fault in the dynamic part of such systems with model uncertainties. When certain conditions are satisfied, the weight vector of the rational square-root B-spline model proves to be bounded. Conver- gency analysis is performed for the error dynamic system raised from robust fault detection and fault diagnosis phase. Computer simulations are given to demon- strate the effectiveness of the proposed algorithm.     

Design of robust model predictive control with input constraints

This article addresses the problem of designing a robust output feedback model predictive control (MPC) with input constraints, which ensures a parameter-dependent quadratic stability and guaranteed cost for the case of linear polytopic systems. A new heuristic method is introduced to guarantee input constraints for the MPC. To reject disturbances and maintain the process at the optimal operating conditions or setpoints, the integrator is added to the controller design procedure. Finally, some numerical examples are given to illustrate the effectiveness of the proposed method.     

H∞ control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions

This paper presents the issue of robust disturbance attenuation and robust asymptotic stability problem for finite-dimensional linear parameter-dependent state-delayed systems. The use of polynomial parameter-dependent quadratic Lyapunov functions and linear matrix inequalities (LMIs) formulations for robust H _∞ control are considered. It is shown that the state feedback control can be determined to guarantee the stability of the closed-loop system independently of the time-delay. We present an illustrative example to demonstrate the applicability of the proposed design approach.     

Parameter-dependent robust H ∞ filter design for uncertain discrete-time systems with quantized measurements

This paper deals with the problem of parameter-dependent robust H _∞ filter design for uncertain discrete-time systems with output quantization. The uncertain parameters are supposed to reside in a polytope. The system outputs are quantized by a memoryless logarithmic quantizer before being transmitted to a filter. Attention is focused on the design of a robust H _∞ filter to mitigate quantization effects and ensure a prescribed H _∞ noise attenuation level. Via introducing some slack variables and using the parameter-dependent Lyapunov function, sufficient conditions for the existence of a robust H _∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Peak-to-peak filtering for periodic piecewise linear polytopic systems

In this paper, the robust peak-to-peak filtering problem for periodic piecewise systems with polytopic uncertainties is investigated. Attention is focused on designing of robust peak-to-peak filters that guarantee the robust asymptotic stability of periodic piecewise filtering error system and satisfy a prescribed peak-to-peak disturbance attenuation level for all admissible uncertainties. A sufficient condition is proposed for robust stability and peak-to-peak performance by employing the constructed time-varying Lyapunov function. Two design approaches based on the Lyapunov function with parameter-dependent matrices and parameter-independent matrices are utilised to solve this problem. An algorithm is proposed to compute the periodic filter parameters governed by non-convex feasibility conditions. Two numerical examples are presented to demonstrate the effectiveness of the proposed techniques.