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Shape control on probability density function in stochastic systems

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Journal of Systems Engineering and Electronics 2014年第1期25卷 144-149页

作者： Lingzhi Wang fucai qian Jun Liu School of Automation and Information Xi'an University of Technology School of Automation Xi'an University of Posts and Telecommunications State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University

A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.

关键词： stochastic systems probability density function (PDF),shape control improved particle swarm optimization.

Robust adaptive control for dynamic systems with mixed uncertainties

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Journal of Systems Engineering and Electronics 2016年第3期27卷 656-663页

作者： Jiaoru Huang fucai qian Guo Xie Hengzhan Yang School of Automation and Information Engineering Xi'an University of Technology Key Laboratory of Spacecraft In-orbit Fault Diagnosis and Repair Xi'an Satellite Control Center

The control problem for single-input single-output（SISO） systems in the presence of mixed uncertainties, both stochastic and deterministic uncertainties, is considered. The stochastic uncertainties are modeled as exogenous noises, while the deterministic uncertainties are time invariant and appear as the unknown parameters which lie in a bounded interval. Based on a subdivision for the continuous interval, a robust adaptive controller is designed. The controller can not only realize the system output to track the desired output, but also learn a more accurate interval which contains the true value of the unknown parameter with a learning error given in advance. An example is given finally to demonstrate the effectiveness of the proposed method.

关键词： stochastic uncertainties deterministic uncertainties minimum variance control robust control robust adaptive control

A Novel PDF Shape Control Approach for Nonlinear Stochastic Systems

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IEEE/CAA Journal of Automatica Sinica 2022年第8期9卷 1490-1498页

作者： Lingzhi Wang Guo Xie fucai qian Jun Liu Kun Zhang Electrical Engineering Department School of AutomationXi’an University of Posts and TelecommunicationsXi’an 710121China School of Automation and Information Engineering Xi’an University of TechnologyXi’an 710048China

In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is ***,we provide the formula for the PDF shape controller without devising the control law of the ***,based on the exact analytical solution of the Fokker-PlanckKolmogorov(FPK)equation,the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state *** validate the performance of the proposed control approach,we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation *** results show that the novel PDF shape control approach is effective and *** an equal number of parameters,our method can achieve a similar or better control effect as the exponential polynomial *** comparison with the multiGaussian closure method,our method has clear advantages in PDF shape control *** all cases,the integral of squared error and the errors of first four moments of our proposed method were very small,indicating superior performance and promising good overall control effects of our *** approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.

关键词： Fokker-Planck-Kolmogorov(FPK)equation nonlinear control nonlinear stochastic systems probability density function(PDF)

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稳态大系统中关联平衡法的改进

系统工程理论与实践 1998年第8期18卷 87-90页

作者：钱富才万百五西安交通大学系统工程研究所

对于子系统的性能指标按一定顺序耦合的稳态大系统，本文采用两级递阶优化控制算法。利用上下级之间的纵向信息交换对子系统之间的关联进行解耦，利用子系统之间的横向信息传递对目标函数进行解耦，这种方法是对关联平衡法的改进，从而... 详细信息

对于子系统的性能指标按一定顺序耦合的稳态大系统，本文采用两级递阶优化控制算法。利用上下级之间的纵向信息交换对子系统之间的关联进行解耦，利用子系统之间的横向信息传递对目标函数进行解耦，这种方法是对关联平衡法的改进，从而，解决了一类不可分的稳态优化问题，仿真效果好。

关键词：大系统稳态优化递阶控制关联平衡法

The probability density function adjust for uncertain stochastic systems

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The probability density function adjust for uncertain stocha...

第37届中国控制会议

作者： Hengzhan Yang Yueyuan Fu fucai qian School of Electronics and Information Engineering Xi'an Technological University School of Automation and Information Engineering Xi'an University of Technology

For nonlinear stochastic systems,aprobability density function adjust algorithm is presented in this ***,the state equation and the control equation are supposed to be the polynomial form,and an exponential form is used to represent probability density ***,the equations with respect to Taylor series expansion coefficients and adjust gain according to the parameter relationships under steady-state conditions is obtained from FPK ***,the corresponding relationship between Taylor expansion coefficients and the polynomial coefficients of the control equation can be obtained through solving the *** an optimization problem of track-target probability density function is *** obtaining the optimization solution,the adjust gain can be ***,examples show the effectiveness of the proposed method.

关键词： Nonlinear stochastic systems Probability density function FPK equation

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基于支持向量机模糊推理的二级倒立摆控制

仪器仪表学报 2008年第2期29卷 330-335页

作者：刘涵周党伟钱富才西安理工大学自动化与信息工程学院西安710048

本文提出了一种用于非线性系统控制的支持向量机模糊推理模型。该模型利用支持向量机回归的原理,从训练数据中提取模糊规则并进行简化;采用核函数来描述模糊推理系统,该模糊推理系统具有不必事先确定模糊规则数目、良好的泛化能力等优... 详细信息

本文提出了一种用于非线性系统控制的支持向量机模糊推理模型。该模型利用支持向量机回归的原理,从训练数据中提取模糊规则并进行简化;采用核函数来描述模糊推理系统,该模糊推理系统具有不必事先确定模糊规则数目、良好的泛化能力等优点。使用该模型对直线二级倒立摆系统构造模糊控制器并进行了实验研究,研究结果表明这种新的模糊规则提取方法对于非线性系统的控制是有效的,由支持向量确定的模糊规则不会出现规则数目'爆炸'的问题,该方法在不便事先确定模糊规则的复杂非线性系统控制中有着重要的应用价值。

关键词：非线性控制支持向量机模糊基函数倒立摆

Adaptive Generalized Projective Synchronization of a New Fractional Chaotic System with uncertain parameters

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Adaptive Generalized Projective Synchronization of a New Fra...

Dual control for stochastic systems with multiple uncertainties

第30届中国控制与决策会议

作者： Jiaoru Huang Kun Zhong fucai qian The International Joint Research Center of Autonomous Systems and Intelligent Control Xi'an Technological University Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing Xi'an University of Technology

This paper investigates the generalized projective synchronization scheme of a new fractional chaotic system, which can display a four-wing chaotic attractor when the order of system is in the range of 0.82 and ***, considering the situation with unknown parameters, an adaptive nonlinear controller is obtained for synchronization and parameters identification based on fractional-order Lyapunov stability theorem. The fractional-order adaptation law, which can update parameters estimation errors online, is derived to ensure the stability of synchronization error system. Numerical simulations are used to verify the results.

关键词： Four-wing chaotic attractors uncertain parameter generalized projective synchronization parameter identification

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Dual control for stochastic systems with multiple uncertaint...

基于紧支撑多变量多项式函数的非线性随机系统概率密度函数形状控制方法

第三十九届中国控制会议

作者： Xuehui Ma fucai qian Shiliang Zhang School of Automation and Information Engineering Xi'an University of Technology Autonomous Systems and Intelligent Control International Joint Research Center Xi'an Technological University Xi'an Jiaotong University Xi'an

Uncertainties commonly exist in stochastic systems, and they may seriously affect control quality of the stochastic *** this paper, a novel dual control is proposed, where the uncertainties caused by uncontrolled excitations, model parameter fluctuations and system noises are all taken into consideration. First, an online outlier detection algorithm is proposed and integrated in the control scheme to find the outliers in the uncontrolled excitations. Second, based on the model with uncontrolled excitations, two cost functions showing the dual properties are used to derive the control signal: one cost function represents the system output tracking performance, the other one represents the unknown parameter estimation performance. The minimization of the two cost functions forms a double-objective optimization problem and is solved by a designed perturbation domain around the nominal value. Experiments are carried out, and the results show that the proposed controller bears better performance,especially in cases where outliers exist.

关键词： Uncertainties stochastic systems dual control outlier unknown parameter estimation double-objective optimization

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华南理工大学学报（自然科学版） 2024年第7期52卷 39-52页

作者：王玲芝张坤钱富才西安邮电大学自动化学院陕西西安710121 西安理工大学自动化与信息工程学院陕西西安710048

针对非线性随机系统的概率密度函数(PDF)形状控制问题,文中以FokkerPlanck-Kolmogorov(FPK)方程为研究工具,提出了一种基于紧支撑多变量多项式(CSMP)函数的非线性随机系统PDF形状控制方法。当系统处于稳定状态时,系统的PDF被困在特定的... 详细信息

针对非线性随机系统的概率密度函数(PDF)形状控制问题,文中以FokkerPlanck-Kolmogorov(FPK)方程为研究工具,提出了一种基于紧支撑多变量多项式(CSMP)函数的非线性随机系统PDF形状控制方法。当系统处于稳定状态时,系统的PDF被困在特定的紧凑子空间中,不需要对整个空间进行积分。而CSMP函数在一段连续的空间内非0,满足紧凑子空间的特征。因此,文中将CSMP的线性组合(CSMP-LC)作为FPK方程的稳态近似解逼近目标PDF。首先,采用飞蛾扑火优化(MFO)算法优化CSMP-LC函数的参数;然后,通过对多维稳态FPK方程的每一维状态变量进行积分,确保稳态FPK方程在整个空间中的积分为0;最后,求解出一维和二维非耦合的状态变量PDF形状控制器,并进行了仿真实验。结果表明,对于一维非线性随机系统,文中提出的方法能有效地实现对不同类型目标PDF形状(单峰形状、双峰形状、三峰形状)的控制,且在目标PDF形状为复杂的三峰时,文中方法的均值、方差、峰度和偏度误差均优于其他两种方法。文中方法扩展到二维状态变量非耦合的非线性随机系统时,也能较好地实现对PDF形状的控制,为多变量随机系统的PDF形状控制研究提供了新的思路。同时,CSMP函数可以减少积分计算的复杂性,降低了非线性随机系统的PDF形状控制器的求解难度。

关键词： Fokker-Planck-Kolmogorov方程非线性随机系统概率密度函数紧支撑多变量多项式