Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances.The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms.Based on the internal model principle,a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances.According to the sensitivity approach,the optimal tracking control law for the ith nonlinear subsystem can be obtained.The optimal tracking control law for the nonlinear large-scale systems can be obtained.A numerical simulation shows that the method is effective.

New sigma point filtering algorithms for nonlinear stochastic systems with correlated noises

New sigma point filtering algorithms,including the unscented Kalman filter(UKF) and the divided difference filter(DDF),are designed to solve the nonlinear filtering problem under the condition of correlated noises.Based on the minimum mean square error estimation theory,the nonlinear optimal predictive and correction recursive formulas under the hypothesis that the input noise is correlated with the measurement noise are derived and can be described in a unified framework.Then,UKF and DDF with correlated noises are proposed on the basis of approximation of the posterior mean and covariance in the unified framework by using unscented transformation and second order Stirling's interpolation.The proposed UKF and DDF with correlated noises break through the limitation that input noise and measurement noise must be assumed to be uncorrelated in standard UKF and DDF.Two simulation examples show the effectiveness and feasibility of new algorithms for dealing with nonlinear filtering issue with correlated noises.

An Adaptive Sliding Mode Tracking Controller Using BP Neural Networks for a Class of Large-scale Nonlinear Systems

A new type controller, BP neural-networks-based sliding mode controller is developed for a class of large-scale nonlinear systems with unknown bounds of high-order interconnections in this paper. It is shown that decentralized BP neural networks are used to adaptively learn the uncertainty bounds of interconnected subsystems in the Lyapunov sense, and the outputs of the decentralized BP neural networks are then used as the parameters of the sliding mode controller to compensate for the effects of subsystems uncertainties. Using this scheme, not only strong robustness with respect to uncertainty dynamics and nonlinearities can be obtained, but also the output tracking error between the actual output of each subsystem and the corresponding desired reference output can asymptotically converge to zero. A simulation example is presented to support the validity of the proposed BP neural-networks-based sliding mode controller.

From Nothing to Something Ⅱ： Nonlinear Systems via Consistent Correlated Bang

The Chinese ancient sage Laozi said that everything comes from ＇nothing＇. In the work [Chin. Phys. Lett. 30？（2013）？080202], infinitely many discrete integrable systems have been obtained from nothing via simple principles （Dao）. In this study, a new idea, the consistent correlated bang, is introduced to obtain nonlinear dynamic systems including some integrable ones such as the continuous nonlinear Schr？dinger equation, the （potential） Korteweg de Vries equation, the （potential） Kadomtsev–Petviashvili equation and the sine-Gordon equation. These nonlinear systems are derived from nothing via suitable ＇Dao＇, the shifted parity, the charge conjugate, the delayed time reversal, the shifted exchange, the shifted-parity-rotation and so on.

Adaptive Decentralized Asymptotic Tracking Control for Large-Scale Nonlinear Systems With Unknown Strong Interconnections

An adaptive decentralized asymptotic tracking control scheme is developed in this paper for a class of large-scale nonlinear systems with unknown strong interconnections,unknown time-varying parameters,and disturbances.First,by employing the intrinsic properties of Gaussian functions for the interconnection terms for the first time,all extra signals in the framework of decentralized control are filtered out,thereby removing all additional assumptions imposed on the interconnec-tions,such as upper bounding functions and matching conditions.Second,by introducing two integral bounded functions,asymptotic tracking control is realized.Moreover,the nonlinear filters with the compensation terms are introduced to circumvent the issue of“explosion of complexity”.It is shown that all the closed-loop signals are bounded and the tracking errors converge to zero asymptotically.In the end,a simulation example is carried out to demonstrate the effectiveness of the proposed approach.

Robust non-fragile control for discrete-delay nonlinear large-scale systems

Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.

STABILITY OF NONLINEAR COMPARISON EQUATIONS FOR DISCRETE LARGE-SCALE SYSTEMS

On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability for discrete nonlinear autonomous comparison equations are completely established. Among them, a criterion for asymptotic stability is not only sufficient, but also necessary, from which a criterion on the function class C, is derived. Both of them can be used to determine the unexponential stability, even in the large, for discrete nonlinear (autonomous or nonautonomous) systems. All the criteria are of simple algebraic forms and can be readily used.

Model predictive control synthesis algorithm based on polytopic terminal region for Hammerstein-Wiener nonlinear systems

An improved model predictive control algorithm is proposed for Hammerstein-Wiener nonlinear systems.The proposed synthesis algorithm contains two parts:offline design the polytopic invariant sets,and online solve the min-max optimization problem.The polytopic invariant set is adopted to replace the traditional ellipsoid invariant set.And the parameter-correlation nonlinear control law is designed to replace the traditional linear control law.Consequently,the terminal region is enlarged and the control effect is improved.Simulation and experiment are used to verify the validity of the wind tunnel flow field control algorithm.

H_(∞)output feedback control for large-scale nonlinear systems with time delay in both state and input

The H_(∞)output feedback control problem for a class of large-scale nonlinear systems with time delay in both state and input is considered in this paper.It is assumed that the interconnected nonlinearities are limited by constant multiplied by unmeasured states,delayed states and external disturbances.Different from existing methods to study the H_(∞)control of large-scale nonlinear systems,the static gain control technique is utilized to obtain an observer-based output feedback control strategy,which makes the closed-loop system globally asymptotically stable and attenuates the effect of external disturbances.An example is finally carried out to show the feasibility of the proposed control strategy.

基于相关分析和带遗忘因子的随机梯度的非线性系统Wiener模型辨识

实际工业过程往往呈现强非线性和时滞特性,在复杂工况下如何建立过程的高精度模型并对其进行有效控制是研究重点.本文研究了一种基于相关分析的非线性系统Wiener模型辨识.Wiener非线性模型由动态线性子系统和静态非线性子系统串联组成,利用时滞状态空间模型和神经模糊模型分别建立动态线性子系统和静态非线性子系统,并利用设计的组合信号实现Wiener非线性模型分离辨识.首先,利用后移算子的性质,将时滞状态空间模型转化为传递函数模型,在高斯信号作用下利用相关分析方法辨识动态线性子系统的参数,解决了Wiener模型中间变量不可测问题.其次,为了改善辨识模型的精度和收敛速度,推导了带遗忘因子的递推随机梯度方法,得到静态非线性子系统的参数估计.将提出的非线性Wiener模型辨识方法运用于连续搅拌反应釜,实验仿真结果表明,本文提出的Wiener模型辨识方法能够有效辨识连续搅拌反应釜系统,并取得较好的控制效果.

自构建关联噪声下的随机共振及其在故障诊断上的应用

轴承作为旋转机械的重要组件之一,及时对其进行健康监测与更换可有效避免设备停机,减少经济损失。首先基于自构建关联噪声驱动下的随机共振系统(stochastic resonance system driven by self-constructingly correlated noise, DSCSR),推导了在正弦激励下该系统输出的理论信噪比(signal-to-noise ratio, SNR)。研究发现通过调节此非线性系统的参数可观察到随机共振现象。其次,针对将随机共振现象用于故障诊断时需要准确的先验知识这一局限性,进一步提出了基于功率谱的信噪比评价指标,并以此来确定非线性系统随机共振发生时的最优系统参数,对最优参数系统输出信号进行功率谱分析来判断故障类型。最后,通过轴承故障诊断试验以及实际风机轴承内圈故障实例证明了DSCSR方法的有效性,以及其增强微弱故障特征并抑制其他谐波以及噪声的干扰的能力。

一类带有输入时滞的非线性关联大系统的分散自适应控制

为解决带有完全未知关联项和输入时滞的非线性关联大系统的跟踪控制问题,本文提出一种自适应分散控制策略,利用神经网络逼近理论处理未知项,同时引入合适的辅助系统消除输入时滞。为了消除未知关联项对系统的影响,定义新的未知常数和非线性光滑函数来界定未知关联项。根据Lyapunov稳定性理论,本文所提出的控制方法能够保证闭环系统一致最终有界,并且跟踪误差能够收敛到原点的一个小邻域内。最后通过仿真算例进一步检验所设计方法的可行性。

Parametric Estimation of Interconnected Nonlinear Systems Described by Input-output Mathematical Models

In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.

The Approximate Solutions of FPK Equations in High Dimensions for Some Nonlinear Stochastic Dynamic Systems

The probabilistic solutions of the nonlinear stochastic dynamic(NSD)systems with polynomial type of nonlinearity are investigated with the subspace-EPC method.The space of the state variables of large-scale nonlinear stochastic dynamic system excited by white noises is separated into two subspaces.Both sides of the Fokker-Planck-Kolmogorov(FPK)equation corresponding to the NSD system is then integrated over one of the subspaces.The FPK equation for the joint probability density function of the state variables in another subspace is formulated.Therefore,the FPK equation in low dimensions is obtained from the original FPK equation in high dimensions and it makes the problem of obtaining the probabilistic solutions of largescale NSD systems solvable with the exponential polynomial closure method.Examples about the NSD systems with polynomial type of nonlinearity are given to show the effectiveness of the subspace-EPC method in these cases.

Correlation Functions of an Autonomous Stochastic System with Nonlinear Time Delays

The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences between the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonlinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.

广义连续随机非线性系统的状态估计问题

讨论了系统噪声和测量噪声为非零均值及具有相关噪声干扰情形下的广义连续随机非线性系统 ,利用矩阵的奇异值分解方法 。

噪声相关粒子滤波算法

对标准粒子滤波在处理非线性系统状态估计中噪声独立假设的局限,该文研究分析了一种噪声相关粒子滤波算法。在常用的系统状态模型基础上,分析了噪声相关时建议分布函数的具体分布形式,并以高斯相关噪声为背景,在重要性权重条件最小方差意义下推导了最优建议分布函数的数值表达式。所设计的滤波器有效弥补了传统粒子滤波算法在噪声相关情况下的缺陷,拓展了PF算法的应用范围。仿真实验表明了该方法的有效性。

基于KCCA虚假邻点判别的非线性变量选择

特征变量选择技术是非线性系统建模过程中降低信息冗余和提高精度的有效方法。提出一种结合核典型相关法(kernel canonical correlation analysis,KCCA)与虚假最近邻法的变量选择法。首先引入核方法,将非线性原始数据映射到线性空间,再采用典型相关法有效合理地消除因子之间的多重共线性,受混沌相空间虚假最近邻点法的启示,通过计算原始数据在KCCA子空间中投影的距离,判断其对主导变量的解释能力,由此进行变量的选择。该方法用氢氰酸生产工艺工程中的非线性模型验证,并与全参数模型进行比较,结果显示该方法有良好的变量选择能力。因此,该研究为非线性系统建模的变量选择方法提供了一种新方法。

蚂蚁算法在日用水量预测中的应用研究

城市日用水量预测是城市供水管网系统动态模拟的基础和前提,用神经网络对城市日用水量预测的非线性回归组合模型求解的过程中,提出了采用新型的仿生算法——蚂蚁算法来训练神经网络的权值.此方法简化了训练过程,避免了BP算法易陷于局部极值等问题.将经过蚂蚁算法训练的神经网络应用到S.X市日用水量预测模型中,显示了此网络模型具有良好的预测能力,验证了基于蚂蚁算法的神经网络在城市日用水量的预测中具有有效性和可行性.

基于贝叶斯估计噪声相关下的CKF设计

针对常规容积卡尔曼滤波(cubature Kalman filter,CKF)要求系统噪声和量测噪声必须互不相关的局限性,提出了一种带相关噪声的非线性离散系统CKF设计方法。基于贝叶斯估计准则,给出了系统噪声和量测噪声相关时CKF滤波递推公式,并采用三阶球面-相径容积规则来近似计算系统状态的后验均值和协方差。当系统噪声和量测噪声相关时,常规CKF不适用,本文设计的噪声相关下的CKF可以有效地对状态进行估计,拓展了CKF的应用范围。数值仿真验证了算法的有效性。