线性时滞系统基于观测器的最优输出跟踪控制器近似设计

研究线性时滞系统的最优输出跟踪控制器近似设计过程.首先根据原系统最优输出跟踪控制问题构造了两个分别具有已知初始条件和终端条件的微分方程迭代序列,并证明它们一致收敛于原问题的最优解.然后通过对该解序列的有限次迭代,得到最优输出跟踪控制问题的一个近似解,进一步给出一个计算近似最优输出跟踪控制律的算法.最后通过构造降维参考输入观测器解决了最优输出跟踪控制器中前馈项的物理可实现问题.仿真结果表明该方法是有效的,且易于实现.     

时变不确定性系统的二自由度最优鲁棒稳态跟踪控制器设计

研究了被控系统存在范数有界的时变模型摄动和未知外部干扰时鲁棒稳态跟踪问题. 利用二自由度控制结构和Youla参数化方法.提出了一个最坏情况稳态绝对误差的精确计算公 式,利用该公式最优稳态跟踪控制器设计问题可化为一个有限维l1优化问题.因此控制器设计 只需解一个标准线性规划问题.此外,还证明了所提出的控制器可同时保证系统的鲁棒稳定性 和最优跟踪性能.仿真结果表明了该方法的有效性和可行性.     

基于信息融合的离散系统最优预见重复控制

针对现有控制器中预见补偿器和重复控制器相对独立作用的最优跟踪问题,提出从信息融合的角度构造线性离散系统的最优预见重复控制器的设计方法.首先,在离散系统中引入L阶差分算子,将预见重复控制设计问题转化为调节稳定性问题;然后,使用协状态和信息量的概念获得控制软约束信息来描述最优融合的过程,得到控制增量信息和增广误差系统协状态的最优估计滤波;最后,将有关预见重复控制器控制律所有信息融合,得到由状态反馈、重复控制和预见补偿构成的最优预见重复控制器.数字仿真结果表明,与独立的最优预见重复控制器相比,基于信息融合的最优预见重复控制器在更少的周期内达到稳定,且在有限的步数下,更能有效利用系统的未来有效信息,从而大幅提高跟踪精度.     

互质因子摄动下的最优鲁棒稳态跟踪控制器设计

研究了存在未知外部干扰时的互质因子摄动系统的鲁棒稳态追踪问题.利用Youla参数化方法，提出了一个最坏情况稳态绝对误差的精确计算公式.该公式使得最优稳态跟踪控制器设计问题等价于保证系统鲁棒稳定时e1的最优鲁棒控制器设计问题.     

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l_∞范数和l_1范数最小化的二自由度最优鲁棒跟踪控制

研究了具有乘摄动模型不确定性并存在未知干扰系统的最优鲁棒跟踪控制问题 .采用二自由度控制器结构Youla参数化方法将最优鲁棒跟踪控制问题转化为两个相互独立的优化问题 :跟踪问题和鲁棒设计问题 .跟踪问题以l∞ 范数为性能指标通过极小化跟踪误差的最大幅值实现最优跟踪控制 ;鲁棒性设计问题中 ,将模型不确定性视为一种外界干扰 ,通过极小化干扰到误差的灵敏度函数的l1范数使得干扰对跟踪误差的影响最小 .通过截断处理 ,上述两种优化问题均可化为标准线性规划问题 .给出了截断阶数与逼近误差之间的关系 .仿真结果表明新方法的有效性 .     

输出概率密度函数的最优跟踪控制:均方根B - 样条模型

在分析均方根B样条模型在实现输出概率密度函数最优跟踪控制时存在的问题的基础上,提出了将最优跟踪控制转化为非线性状态约束下的跟踪误差最优调节器,然后依据非线性状态约束和系统模型的特点分别设计了鲁棒变结构控制器及非线性观测器,并利用误差补偿控制来保证非线性观测器误差的有界性.仿真结果表明了提出的转换控制策略的有效性.     

基于l∞范数和l1范数最小化的二自由度最优鲁棒跟踪控制

研究了具有乘摄动模型不确定性并存在未知干扰系统的最优鲁棒跟踪控制问题,采用二自由度控制器结构Youla参数化方法将最优鲁棒跟踪控制问题转化为两个相互独立的优化问题,跟踪问题和鲁棒设计问题,跟踪问题以l∞范数为性能指标通过极小化跟踪误差的最大幅值实现最优跟踪控制;鲁棒性设计问题中,将模型不确定性视为一种外界干扰,通过极小化干扰到误差的灵敏度函数的l1范数使得干扰对跟踪误差的影响最小,通过截断处理,上述两种优化问题均可化为标准线性规划问题,给出了截断阶数与逼近误差之间的关系,仿真结果表明新方法的有效性。     

基于信息融合估计的离散系统最优跟踪控制

针对期望输出和未来干扰无预见的离散线性系统最优跟踪问题,提出一种基于信息融合最优估计的控制方法.若将当前给定值和可测干扰值分别看作系统未来输出和干扰的预见值,则跟踪控制问题可转化为具有无限预见步数的预见控制问题,并将无限预见信息融合成一步等效预见信息,进而获得近似最优融合控制律.对线性直流电机系统和宏观经济系统的仿真结果均验证了该控制器在提高系统跟踪精度和抑制干扰等方面的有效性.     

风扰影响下的无人机非线性广义最小方差跟踪控制

本文以鱼鹰型固定翼无人机为研究对象,基于非线性广义最小方差(nonlinear generalized minimum variance,NGMV)最优控制理论,研究了受到非线性阵风干扰影响下的无人机跟踪控制问题.首先对鱼鹰型无人机动力学模型解耦,在解耦后的横向和纵向模型上分别实现跟踪控制;然后针对阵风非线性模型的特定形式,根据NGMV理论设计了增维的非线性广义最小方差控制器,使得模型充分考虑了阵风干扰的特性.所设计的NGMV最优控制器的主要优势在于它能处理带有干扰和时滞环节的非线性系统.多组阵风扰动的仿真试验结果表明,非线性广义最小方差最优控制器具有跟踪性和收敛性.     

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.     

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.     

Cooperative optimal preview tracking control of continuous-time multi-agent systems

This paper presents the cooperative preview control method for continuous-time multi-agent systems with a time-invariant directed communication topology. First, the cooperative tracking preview control problem is transformed into the optimal regulation problem of an augmented system. Next, by applying the results of the standard optimal preview control of continuous-time linear systems, a controller of the augmented system is obtained. Furthermore, the stabilisability and detectability of the augmented system are studied under the fixed digraph and the prescribed leader. Then, we derive the controller of multi-agent systems with error integral and preview action that can guarantee the achievement of cooperative optimal preview tracking. Finally, the effectiveness of the controller is shown by numerical simulations.     

Optimal Decoupling Control Method and Its Application to a Ball Mill Coal-pulverizing System

The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method is proposed, which can simultaneously provide optimal performance. The optimal decoupling controller is composed of an inner-loop decoupling controller and an outer-loop optimal tracking controller. First, by introducing one virtual control variable, the original differential equation on state is converted to a generalized system on output. Then, by introducing the other virtual control variable, and viewing the coupling terms as the measurable disturbances, the generalized system is open-loop decoupled. Finally, for the decoupled system, the optimal tracking control method is used. It is proved that the decoupling control is optimal for a certain performance index. Simulations on a ball mill coal-pulverizing system are conducted. The results show the effectiveness and superiority of the proposed method as compared with the conventional optimal quadratic tracking (LQT) control method.      

具有解耦性能的离散时间线性多变量系统最优跟踪控制

在传统线性二次跟踪控制方法的基础上, 针对一类具有强耦合特性的离散时间线性多变量系统, 提出了一种具有解耦性能的最优跟踪控制方法. 首先为实现解耦, 将耦合项作为可测干扰, 基于零和博弈思想提出了一种新的性能指标; 然后针对该性能指标, 利用极小值原理设计最优跟踪控制器, 通过适当加权矩阵的选择, 同步实现解耦和跟踪; 最后进行仿真实验, 仿真结果表明了该方法的有效性以及在最优性能等方面的优越性.     

Integral sliding mode based optimal composite nonlinear feedback control for a class of systems

This paper presents an optimization method of designing the integral sliding mode （ISM） based composite nonlinear feedback （CNF） controller for a class of low order linear systems with input saturation. The optimal CNF control is first designed as a nominal control to yield high tracking speed and low overshoot. The selection of all the tuning parameters for the CNF control law is turned into a minimization problem and solved automatically by particle swarm optimization （PSO） algorithm. Subsequently, the discontinuous control law is introduced to reject matched disturbances. Then, the optimal ISM-CNF control law is achieved as the sum of the optimal CNF control law and the discontinuous control law. The effectiveness of the optimal ISM-CNF controller is verified by comparing with a step by step designed one. High tracking performance is achieved by applying the optimal ISM-CNF controller to the tracking control of the micromirror.     

A separation theorem for stochastic control problems with point-process observations

The exact solution is derived for a stochastic optimal control problem involving a linear stochastic plant, quadratic costs, and nonlinear, nongaussian observations. The observations are in the form of a point process in which each point has both a temporal and a spatial coordinate. The state of the stochastic plant influences the intensity of the observed time-space point process. The solution to this dual control problem can be realized with a separated estimator-controller in which the estimator is nonlinear, mean-square optimal, and finite dimensional, and the controller is the certainty equivalent linear controller. Motivation for the stochastic optimal control problem studied here is given in terms of position sensing and tracking for quantum-limited optical communication problems.     

线性连续时滞系统最优预见重复控制

针对一类线性连续时滞系统,提出一种最优预见重复控制设计方法.首先,通过一种等价变换,将被控时滞系统转化为无时滞系统.然后,利用L阶差分算子提升技巧,获得包含状态变量导数和跟踪误差的增广连续系统.在此基础上,通过定义一种新的性能指标,将预见重复控制设计问题转化为连续非自治系统的线性二次调节问题.进一步,基于最优控制理论,得到包含状态反馈、误差积分、重复控制、时滞补偿和预见补偿的最优预见重复控制器.该控制器包含了已有文献的多种控制器形式.最后,通过一个数值仿真实例,说明所提方法的有效性.