基于LMI的参数随机变化系统的概率密度函数控制

针对模型参数在有界区域内随机变化的系统, 基于平方根 B 样条模型, 提出了输出概率密度函数 (Probability density function, PDF) 跟踪控制策略. 目标是控制系统输出的概率密度函数跟踪给定的概率密度函数. 通过 B 样条逼近建立了输出 PDF 和权值之间的对应关系, 把 PDF 的跟踪转化为权值的跟踪, 同时系统转化为 MIMO 系统,从而权值向量的跟踪就转化为 MIMO 系统的跟踪问题, 接着给出了系统输出概率密度函数跟踪给定概率密度函数的控制器存在的充分条件, 通过求解线性矩阵不等式完成状态反馈和输出反馈跟踪控制器的设计, 得到了系统具有 Hinfinity 范数界 Gamma 鲁棒镇定的结果. 仿真结果表明本文提出的控制算法是有效的.     

基于观测器的受扰非线性系统近似最优跟踪控制

研究一类受扰非线性系统的最优输出跟踪控制问题.给出了有限时域最优输出跟踪控制律的近似设计算法.首先将求解受扰非线性系统最优跟踪控制问题转换为求解状态向量与伴随向量耦合的非线性两点边值问题,然后利用逐次逼近方法构造序列将其转化为求解两个解耦的线性微分方程序列问题.通过迭代求解伴随向量的序列,可得到由解析的线性前馈-反馈控制部分和伴随向量的极限形式的非线性补偿部分组成的最优输出跟踪控制律.利用参考输入降维观测器和扰动降维观测器,解决了前馈控制的物理可实现问题.最后仿真结果表明了该方法的有效性.     

输出概率密度函数鲁棒弹性最优跟踪控制

研究了一类随机动态系统的鲁棒弹性最优跟踪控制问题。在采用B样条神经网络模型逼近随机动态系统的输出概率密度函数(PDF)的基础上,同时考虑系统模型和控制器增益不确定性,结合Lyapunov稳定性理论和线性矩阵不等式(LMI)技术,引入增广控制作用,设计基于广义状态反馈的鲁棒弹性最优跟踪控制器,目的是使系统的输出PDF跟踪给定PDF。通过求解LMI,所得控制器不仅能实现跟踪目的,而且能确保该随机动态系统全局稳定并满足一定的线性二次型性能指标上界。仿真结果表明该方法简单易行,且无需任何设计参数调整。     

基于线性参数神经网络的非线性系统稳定自适应控制

提出适用于多种网络类型的神经网络稳定自适应控制设计思想,在神经网络逼近误差界未知的条件下,对该误差界进行在线自适应估计,研究基于线性参数神经网络的仿射非线性系统稳定自适应控制。采和Ｌａｐｕｎｏｖ函数方法证明系统状态变量、网络权值矢量、网络逼近误差界的在线估计及输出跟踪误差的收敛性。仿真结果表明,该方案跟踪性能良好,稳态误差较小,系统输出能快速跟踪目标信号。     

时变不确定非线性系统自适应滑模跟踪控制

针对一般的具有时变且界未知的非线性不确定性的单输入多输出非线性系统．提出一种自适应滑模跟踪控制器的框架。在该框架内,系统的时变且界未知的非线性不确定性可以通过函数逼近技术（FAT）表示成为一组正交基函数序列的组合,并通过滑模控制技术和直接Lyapunov方法获得基函数系数的更新律以及对不确定性逼近误差的在线自适应补偿,从而得到自适应的滑模控制律。所提出的基于函数逼近技术的自适应滑模跟踪控制策略在直流电机跟踪控制系统实验装置上进行了实际控制实验,并进行了性能的对比与分析。     

采用观测器的双线性系统最优跟踪控制器设计

研究一类参考输入由外系统描述的双线性系统的最优输出跟踪控制问题.利用逐次逼近的方法,首先构造一族非齐次线性两点边值问题序列将原非线性两点边值问题解耦;然后迭代求解伴随向量的序列,得到由状态向量的线性解析函数和以伴随向量的极限形式给出的非线性部分的补偿项组成的最优输出跟踪控制律.通过构造降维观测器重构外系统的状态,解决了最优输出跟踪控制律的物理可实现问题仿真结果表明了该方法的有效性.     

纵列式无人直升机建模及其精确线性化方法研究

利用牛顿-欧拉法对纵列式无人直升机的近似悬停模态进行数学建模，得出标准仿射非线性状态方程，然后应用状态反馈精确线性化方法进行设计．仿真结果表明，系统输出可稳定跟踪给定信号．     

基于自适应动态规划的非线性鲁棒近似最优跟踪控制

为克服现有近似最优跟踪控制方法只能跟踪连续可微参考输入的局限,本文针对一类具有未知动态的连续时间非线性时不变仿射系统,提出了一种新的基于自适应动态规划的鲁棒近似最优跟踪控制方法.首先采用递归神经网络建立系统模型,然后建立评价神经网络对最优性能指标进行估计,从而得到最优性能指标偏导数的估计值,进而得到近似最优跟踪控制器,最后利用系统输出与参考输入之间的跟踪误差设计鲁棒项对神经网络建模误差进行补偿.分别针对两个非线性系统进行仿真实验,仿真结果表明了所提方法的有效性和优越性.     

时变不确定非线性系统自适应滑模跟踪控制

针对一般的具有时变且界未知的非线性不确定性的单输入多输出非线性系统,提出一种自适应滑模跟踪控制器的框架.在该框架内,系统的时变且界未知的非线性不确定性可以通过函数逼近技术(FAT)表示成为一组正交基函数序列的组合,并通过滑模控制技术和直接Lyapunov方法获得基函数系数的更新律以及对不确定性逼近误差的在线自适应补偿,从而得到自适应的滑模控制律.所提出的基于函数逼近技术的自适应滑模跟踪控制策略在直流电机跟踪控制系统实验装置上进行了实际控制实验,并进行了性能的对比与分析.     

一类双线性系统的最优跟踪控制问题

针对一类具有二次型性能指标的双线性系统的最优跟踪控制问题,提出了一种通过逐次逼近法设计最优控制律的近似方法。首先将状态向量含有时滞的双线性系统的最优跟踪问题转化为最优调节问题;然后利用逐次逼近算法,将既含有时滞项又含有超前项的两点边值问题转化为不含时滞项和超前项的线性两点边值问题族,得到调节系统的最优控制律,并可以通过截取最优控制序列的有限项得到调节系统的前馈-反馈次优控制律。最后,将最优控制问题转化为最优跟踪问题。仿真结果表明,此方法达到了较好的跟踪效果。     

Multi-objective PID control for non-Gaussian stochastic distribution system based on two-step intelligent models

A new method for controlling the shape of the conditional output probability density function (PDF) for general nonlinear dynamic stochastic systems is proposed based on B-spline neural network (NN) model and T-S fuzzy model. Applying NN approximation to the measured PDFs, we transform the concerned problem into the tracking of given weights. Meanwhile, the complex multi-delay T-S fuzzy model with exogenous disturbances, parametric uncertainties and state constraints is used to represent the nonlinear weigh...     

Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

This article presents a new proportional-integral (PI) tracking control strategy for non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Following the square root B-spline approximation to the measured output PDF, a non-linear discrete-time dynamical model can be established between the control input and the weights related to the PDFs. It is noted that the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics. For the non-linear discrete-time weight model including time-delay terms and exogenous disturbances, convex linear matrix inequality optimisation algorithms are used to design a generalised PI controller such that stabilisation, state constraint and tracking performance can be guaranteed simultaneously. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimise the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

PID controller design for output PDFs of stochastic systems using linear matrix inequalities

This paper presents a pseudo proportional-integral-derivative (PID) tracking control strategy for general non-Gaussian stochastic systems based on a linear B-spline model for the output probability density functions (PDFs). The objective is to control the conditional PDFs of the system output to follow a given target function. Different from existing methods, the control structure (i.e., the PID) is imposed before the output PDF controller design. Following the linear B-spline approximation on the measured output PDFs, the concerned problem is transferred into the tracking of given weights which correspond to the desired PDF. For systems with or without model uncertainties, it is shown that the solvability can be casted into a group of matrix inequalities. Furthermore, an improved controller design procedure based on the convex optimization is proposed which can guarantee the required tracking convergence with an enhanced robustness. Simulations are given to demonstrate the efficiency of the proposed approach and encouraging results have been obtained.     

Shaping of Output PDF Based on the Rational Square-root B-spline Model

This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems.At first,a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudo- weights is introduced.The new model is then compared with the existing B-spline models in terms of feasible domains.Next,a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available.Finally,illustrative examples indicate the effectiveness of the proposed algorithms.     

基于有理平方根B样条模型的概率密度函数形状控制

This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems. At first, a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudoweights is introduced. The new model is then compared with the existing B-spline models in terms of feasible domains. Next, a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available. Finally, illustrative examples indicate the effectiveness of the proposed algorithms.     

Constrained PID tracking control for output PDFs of non‐gaussian stochastic system based on LMIs

This paper presents a new PID tracking control strategy for general non‐Gaussian stochastic systems based on a square root B‐spline model for the output probability density functions (PDFs). Using the B‐spline expansion with modeling errors and the nonlinear weight model with exogenous disturbances, the PDF tracking is transformed to a constrained dynamical tracking control problem for weight vectors. Instead of the non‐convex design algorithms, the generalized PID controller structure and the improved convex linear matrix inequality (LMI) algorithms are proposed to fulfil the PDF tracking problem. Meanwhile, in order to enhance robustness, the robust peak‐to‐peak measure is applied to optimize the tracking performance. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Multi-step Predictive Control of a PDF-shaping Problem

A predictive control strategy is proposed for the shaping of the output probability density function (PDF) of linear stochastic systems. The B-spline neural network is used to set up the output PDF model and therefore converts the PDF-shaping into the control of B-spline weights vector. The Diophantine equation is then introduced to formulate the predictive PDF model, based on which a moving-horizon control algorithm is developed so as to realize the predictive PDF tracking performance.     

输出概率密度函数形状的多步预测控制

A predictive control strategy is proposed for the shaping of the output probability density function (PDF) of linear stochastic systems. The B-spline neural network is used to set up the output PDF model and therefore converts the PDF-shaping into the control of B-spline weights vector. The Diophantine equation is then introduced to formulate the predictive PDF model, based on which a moving-horizon control algorithm is developed so as to realize the predictive PDF tracking performance.     

Generalized discrete-time PI control of output PDFs using square root B-spline expansion

A new control approach is proposed for the probability density function (PDF) control of non-Gaussian stochastic systems using PI controllers. Using the square root output PDF model and the weight dynamics, the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics, where LMI techniques are used to design a generalized PI controller such that stability, state constraints and tracking performances can be guaranteed simultaneously.     

基于有理平方根逼近的非高斯随机分布系统的故障诊断和容错控制

随机分布系统指的是输入为常规向量而输出为系统输出的概率密度函数所描述的一类随机系统．该类系统控制算法的目标是选择一个控制输入使得系统的实际输出概率密度函数尽可能跟踪一个事先给定的概率密度函数．本文对采用有理平方根B样条逼近其输出概率密度函数的非高斯动态随机分布系统,提出了一种基于非线性自适应观测器的故障诊断方法．该方法可快速有效地诊断出非高斯随机分布系统故障．通过对故障系统的重组,使故障后系统的输出概率密度函数仍能跟踪给定的分布,实现了该随机系统的容错控制,提高了随机系统的可靠性．