一类受扰不确定混沌系统的最优控制

基于状态反馈精确线性化,研究了具有外界扰动作用下的不确定混沌系统的线性二次型最优控制器设计问题。首先通过微分同胚坐标变换将受扰动混沌系统模型转变为无扰动的伪线性系统模型;然后给出基于二次型性能指标的最优控制器设计方法。与现有方法相比,文中线性二次型问题的最优解不仅可以写成统一的解析表达式而且实现了求解过程的规范化,线性状态反馈控制律简单且便于工程实现,因而广泛应用于实际工程问题中。最后对Liu混沌系统进行仿真,仿真结果证明了该方法的有效性。     

不确定离散时滞分段系统的广义H2弹性控制

针对一类不确定离散时滞分段系统,研究了广义H2稳定性分析和带有时滞的状态反馈弹性控制器设计问题.通过构造适当的离散分段二次李亚普诺夫函数,利用分段二次李亚普诺夫稳定性理论,给出了对于所有的容许参数不确定性,闭环系统是广义H2稳定的充分条件;在此基础上,基于线性矩阵不等式(LMI)处理方法,提出了带有时滞的状态反馈弹性控制器增益阵的设计方案.仿真实例验证了所提方法的有效性.     

基于二维混合模型的保成本重复控制

针对一类线性不确定系统, 提出一种基于二维混合模型的重复控制设计新方法, 研究具有反馈作用的保成本重复控制设计与优化问题. 首先, 为了提高系统稳定性, 将反馈控制器引入到重复控制系统中, 设计一种具有反馈作用的重复控制系统结构; 然后通过建立重复控制系统的连续/离散二维混合模型, 将重复控制器设计问题转化为一类连续/离散二维系统的状态反馈控制问题. 在此基础上, 对给定的线性二次型性能指标, 给出闭环系统的保成本重复控制律参数设计及其优化方法. 对所有容许的不确定性, 保成本重复控制使稳态跟踪误差渐近稳定的同时, 线性二次型性能指标值小于某个常数. 所得结果以线性矩阵不等式的形式给出, 可利用MATLAB工具箱方便地求解.最后, 数值仿真验证了本文所提方法的有效性.     

基于二次稳定的仿真转台鲁棒控制器设计

针对摩擦力矩干扰,系统参数摄动等非线性扰动环节对仿真转台控制系统的影响,提出了基于二次稳定理论的仿真转台鲁棒控制器设计思想。分析了二次稳定理论的基本原理及设计方法,给出了某型飞行仿真转台基于二次稳定的状态反馈控制器和PID鲁棒控制器设计实例。仿真结果表明,基于二次稳定理论的控制器克服了摩擦力矩干扰以及转动惯量摄动对仿真转台的影响,实现了转台转角的精确控制,动态指标优越,满足了高精度飞行仿真转台系统的鲁棒控制要求。     

不确定系统的网络化保性能控制

本文针对控制网络中存在着随机传输时延和数据包丢失的现象,考虑了网络化控制系统的状态反馈保性能控制器设计问题.首先采用时滞相关方法并引入自由权矩阵,给出了基于矩阵不等式的网络化二次型保性能控制器存在的充分条件,然后基于该充分条件获得了基于线性矩阵不等式的控制器设计方法,相应的网络化保性能控制律可以通过求解线性矩阵不等式来构造,并采用锥互补线性化算法给出了网络化次优保性能控制器的设计方法.最后数值示例演示了所得控制器设计结果的应用方法和有效性,并通过仿真比较了传统保性能控制器和网络化保性能控制器在网络化控制系统中的控制性能.     

三级倒立摆的LQG最优控制应用研究

针对三级倒立摆的强耦合不稳定性,应用线性二次型高斯最优控制的方法,设计LQG控制器,对其进行Matlab仿真研究,仿真结果表明,设计的控制器能很好的对倒立摆进行稳定控制,且具有较好的抑制噪声和抗干扰能力.     

多时滞不确定系统的模糊保性能H∞控制

针对多时滞不确定系统,利用T-S模型进行建模,提出了模糊保性能H∞控制问题.基于Lyapunov稳定理论,得到一种通过模糊状态反馈实现的具有干扰抑制的保性能H∞控制.当被控对象存在多时滞和不确定性及外部干扰统计特性未知时,该模糊控制器能保证闭环系统稳定和一定的二次型性能指标上界,同时具有H∞下的干扰抑制作用.控制器的设计可通过转化为线性矩阵不等式的求解问题.数值仿真表明,该控制器具有所期望设计的性能.     

基于风速估计的风力机状态反馈滑模容错控制

针对风力机变桨距执行机构突变故障,提出了基于风速估计的自适应状态反馈滑模容错控制策略.首先,设计了基于自适应状态反馈滑模理论的鲁棒主动容错控制器,并结合全阶补偿器对控制律进行设计;然后,利用基于变速灰狼优化算法的组合径向基函数神经网络实现风速估计,可以改善风速测量精度并提高控制系统可靠性;最后,根据线性矩阵不等式和Lyapunov理论对控制器稳定性进行讨论,并与现有控制策略进行比较.仿真结果表明,在健康/故障的变桨距执行机构条件下,所提容错控制方法均能获得较好的控制效果.     

基于T—S模糊模型的LQR控制器设计

基于T-S模糊模型的平行分配补偿控制器设计方法,结合线性二次型最优控制方法,设计了一个倒立摆系统状态反馈控制器.控制方法有效地将线性系统理论与模糊控制理论结合起来,可处理某些复杂的非线性自不稳定系统控制问题.针对倒立摆是一个非线性、不稳定、强耦合系统,利用MATLAB对其进行仿真实验,结果表明上述方法能够控制倒立摆稳定.TS-LQR控制器结合了模糊控制和LQR方法的优点,具有结构简单、易于实现以及稳定范围大、鲁棒性好的优点,可获得较好的动态性能和稳态性能.     

线性离散时滞系统的输出反馈耗散控制

考虑线性离散时滞系统的二次型耗散控制问题,设计动态输出反馈使闭环系统渐近稳定且严格二次型耗散.先将系统严格二次型耗散性转化为线性矩阵不等式的可解性,得到了系统渐近稳定且严格二次型耗散的条件.然后讨论输出反馈耗散控制问题,给出了控制器的存在条件,总结出了控制器的综合方法、步骤.所得结果可为离散时滞系统的无源控制和H∞控制提供统一框架,也为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

A new optimal multirate control of linear periodic andtime-invariant systems

The optimal multirate design of linear, continuous-time, periodic and time-invariant systems is considered. It is based on solving the continuous linear quadratic regulation (LQR) problem with the control being constrained to a certain piecewise constant feedback. Necessary and sufficient conditions for the asymptotic stability of the resulting closed-loop system are given. An explicit multirate feedback law that requires the solution of an algebraic discrete Riccati equation is presented. Such control is simple and can be easily implemented by digital computers. When applied to linear time-invariant systems, multirate optimal feedback optimal control provides a satisfactory response even if the state is sampled relatively slowly. Compared to the classical single-rate sampled-data feedback in which the state is always sampled at the same rate, the multirate system can provide a better response with a considerable reduction in the optimal cost. In general, the multirate scheme offers more flexibility in choosing the sampling rates     

约束随机线性二次最优控制的研究

本文研究线性终端状态约束下不定随机线性二次最优控制问题.首先利用Lagrange Multiplier 定理得到了存在最优线性状态反馈解的必要条件, 而在加强的条件下也得到了最优控制存在的充分条件. 从某种意义上讲, 以往关于无约束随机线性二次最优控制的一些结果可以看成本文主要定理的推论.     

On a general optimal algorithm for multirate output feedbackcontrollers for linear stochastic periodic systems

A modified optimal algorithm for multirate output feedback controllers of linear stochastic periodic systems is developed. By combining the discrete-time linear quadratic regulation (LQR) control problem and the discrete-time stochastic linear quadratic regulation (SLQR) control problem to obtain an extended linear quadratic regulation (ELQR) control problem, one derives a general optimal algorithm to balance the advantages of the optimal transient response of the LQR control problem and the optimal steady-state regulation of the SLQR control problem. In general, the solution of this algorithm is obtained by solving a set of coupled matrix equations. Special cases for which the coupled matrix equations can be reduced to a discrete-time algebraic Riccati equation are discussed. A reducable case is the optimal algorithm derived by H.M. Al-Rahmani and G.F. Franklin (1990), where the system has complete state information and the discrete-time quadratic performance index is transformed from a continuous-time one     

An example in linear quadratic optimal control

We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme simplicity, this example has all the unexpected features discovered recently by O. Staffans (and also by M. Weiss and G. Weiss). More precisely, in the formula linking the optimal feedback operator to the optimal cost operator, as well as in the Riccati equation, the weighting operator of the input has to be replaced by another operator, which can be derived from the spectral factorization of the Popov function.     

一种新的混沌系统线性反馈最优控制

为了实现一种新的混沌系统的镇定控制且满足给定的性能指标达到极小值。描述了一种新的混沌系统的动力学行为;设计一个二次目标函数,同时根据Pontryagin极小值原理为混沌系统设计一个线性状态反馈最优控制器,所得到的控制律是最优控制,控制器能将混沌系统的轨道从任意初始点出发稳定到零点,控制器结构简单且易于实现。基于Lyapunov稳定性理论证明了系统的稳定性,同时通过对施加闭环控制后的系统状态变化的数值模拟证明了所建议的方法的正确性。     

A patchy approximation of explicit model predictive control

The explicit solution of multi-parametric optimisation problems (MPOP) has been used to construct an off-line solution to relatively small- and medium-sized constrained control problems. The control design principles are based on receding horizon optimisation and generally use linear prediction models for the system dynamics. In this context, it can be shown that the optimal control law is a piecewise linear (PWL) state feedback defined over polytopic cells of the state space. However, as the complexity of the related optimisation problems increases, the memory footprint and implementation of such explicit optimal solution may be burdensome for the available hardware, principally due to the high number of polytopic cells in the state-space partition. In this article we provide a solution to this problem by proposing a patchy PWL feedback control law, which intend to approximate the optimal control law. The construction is based on the linear interpolation of the exact solution at the vertices of a feasible set and the solution of an unconstrained linear quadratic regulator (LQR) problem. With a hybrid patchy control implementation, we show that closed-loop stability is preserved in the presence of additive measurement noise despite the existence of discontinuities at the switch between the overlapping regions in the state-space partition.     

切换控制在倒立摆系统摆起和镇定中的应用

本文针对一级直线型倒立摆对象,基于非线性共振原理和线性二次型最优状态反馈控制,提出了一种基于状态的切换控制策略,实现了倒立摆的快速摆起和镇定。最后通过仿真实验表明,本文提出的方法对一级直线型倒立摆系统的摆起和镇定具有较好效果。     

基于微分对策的最优状态观测器和最优状态反馈控制器的设计

研究了线性系统基于二次型指标的最优状态观测器和最优状态反馈控制器的设计问题．将观测状态的状态反馈和状态误差的输出反馈分别作为两个对局方,应用微分对策理论研究了系统的最优控制问题．给出了最优状态观测器和基于状态观测器的最优状态反馈控制的存在性条件．将系统的最优状态观测器和最优控制器的设计问题转化为一对Riccati方程的求解问题．研究表明最优状态观测器在一般情况下不存在．并进一步研究了基于状态观测器的次优控制问题,给出了基于LMI的优化算法．     

An optimal guidance approximation theory

Synthesis of optimal guidance approximations is undertaken by means of a perturbation theory approach and a scheme for obtaining linear, quadratic and higher order feedback approximations to the optimal control presented. Mechanization is carried out in terms of state deviations from an optimal reference trajectory with the comparison point along the reference selected so that the state comparison is approximately transverse. A simple example is treated analytically, linear and quadratic feedback expressions obtained, and some digital computer simulation results presented which permit a comparison of system performance and accuracy between various approximations.