基于辅助输出的线性系统状态和未知输入同时估计方法

在未知输入观测器匹配条件不满足的情况下, 针对一类线性时不变系统, 研究了同时估计系统 状态和未知输入的问题. 首先, 基于可测输出对未知输入的相关度的概念, 给出了辅助输出 的构造方法, 使得匹配条件得以满足. 为了处理辅助输出中的未知信息, 提出了一种高增益 观测器设计方法, 它不仅能估计辅助输出, 而且还能估计辅助输出的导数. 然后, 基于辅助 输出的估计值, 提出了一种降维观测器设计方法, 可以在不受未知输入影响的情况下估计系统 的状态; 接下来, 基于状态和辅助输出及其导数的估计值, 给出了未知输入估计. 最后, 对一个五 阶系统进行了数字仿真, 仿真结果表明所提出的方法是有效的.     

不确定性时滞系统基于观测器的鲁棒镇定

研究一类不确定性时滞系统的鲁棒镇定问题.当系统既有状态时滞又有控制输入时 滞,而且系统的状态和控制输入均含有不确定性时,假设不确定性满足具有一定物理意义的 匹配条件,得到了系统可由基于观测器的状态反馈鲁棒镇定的充分条件,并给出了观测器和 反馈控制器的设计步骤.该方法仅需求解两个黎卡提不等式.     

约束时变不确定离散系统的输出反馈预测控制综合

研究多包描述系统的离线型输出反馈预测控制．已有一方法首先综合状态反馈预测控制，满足输入/ 状态约束；而在设计观测器时，不再考虑输入/ 状态约束．本文则首先给出观测器，并给出一组不等式条件使得真实状态、观测状态和观测误差都保持在同一个椭圆内部，以便采用线性矩阵不等式处理输入/ 状态约束．基此，本文离线计算一椭圆序列，每个椭圆对应一控制律和一观测器，而在线的实时控制律和观测器则从该序列中选择，使得闭环系统具有稳定性保证．仿真例子说明了本文方法的有效性．     

线性时滞系统故障检测滤波器设计H∞优化方法

研究一类线性时滞系统的基于观测器的故障检测滤波器设计问题.通过对线性时滞系统进行广义坐标变换,得到了只包含输入、输出时滞,无状态时滞的新的系统表达形式.在此基础上,选用基于观测器的故障检测滤波器作为残差产生系统,使得到的残差动态方程为仅包含未知输入时滞和故障时滞的线性时不变形式,进而可应用已取得的线性时不变系统故障诊断研究成果设计故障检测滤波器.同时给出一种线性时滞系统故障检测滤波器设计的H∞优化设计方法,并通过算例验证了所提方法的有效性.     

基于输入输出线性化方法的一类多输入多输出非线性系统的观测器设计

研究一类多输入多输出仿射非线性系统的状态观测器设计问题. 基于输入输出线性化方法提出了一类多输入多输出仿射非线性系统的状态观测器设计的新方法, 并给出保证状态估计误差渐近趋于零的充分条件. 算例表明了所得结果的有效性.     

非方广义系统的未知输入有限时间观测器设计

研究了含未知输入的非方广义系统的有限时间输入解耦观测器设计问题,在一定条件下基于非方广义系统的结构特征,引入一个输入-状态对的非奇异转换,把含未知输入的非方广义系统等价地转化为输入已知的正常状态空间系统．用传统的设计正常状态空间系统观测器的方法去构造含未知输入的非方广义系统的未知输入观测器,并给出了观测器存在的充分条件,由此得出了有限时间观测器的设计步骤．     

基于有限时间观测器的离散系统混沌同步

本文基于驱动–响应模型针对一类离散时间混沌系统提出了一种基于有限时间观测器的同步方法. 首先, 将混沌系统写成具有未知输入的线性系统形式. 随后, 给出了观测器匹配条件和强可观条件. 在观测器匹配条件的 假设下, 通过适当的状态变换, 给出了具有降维形式的有限时间观测器设计框架使得该观测器不再受到未知输入的 影响. 然后, 证明了强可观条件结合观测器匹配条件可以保证一个有限时间观测器的存在, 该观测器可以使得响应 系统达到对驱动系统的精确同步, 且达到同步所需要的时间可以任意设定, 不受观测器系统矩阵极点配置和初值条 件的影响. 最后, 给出了两个混沌系统的例子验证了所提方法的有效性.     

含未知输入的广义系统的状态与输入估计

研究了含未知输入的广义系统的输入解耦观测器设计问题. 在系统脉冲能控的条件下通过系统输入-状态对的非奇异变换, 把此问题等价地转化为正常状态空间系统的相应问题. 用大家熟知的方法设计正常状态空间系统的观测器, 从而得到广义系统的输入解耦观测器. 然后用广义系统的观测器状态和系统输出的线性组合渐近估计系统的状态与未知输入.     

设计最低阶多线性函数观测器的新方法

本文讨论为连续线性时不变多输入多输出系统设计多线性函数观测器的时域方法.用此 法设计的观测器具有最低动态阶数,且极点可以任意配置.本文提供的算法不仅可用于设计 多输出系统的最低阶多线性函数观测器,而且也可用于设计多输出系统的降阶状态观测器.     

一类离散不确定系统的Tube不变集离线鲁棒模型预测控制

针对一类输入和状态受限的离散线性不确定系统,提出了一种基于Tube不变集的离线鲁棒模型预测控制方法.首先针对输入和状态约束线性时不变标准系统,设计了改进的基于多面体不变集的离线模型预测控制算法,并证明了稳定性.其次对于存在未知有界干扰的实际不确定系统,引入了Tube不变集策略,通过设计对应标准模型的最优控制序列和状态轨迹,给出了实际不确定系统的离线Tube不变集控制策略,保证系统状态鲁棒渐近稳定,并收敛于终端干扰不变集.仿真结果验证了该控制方法的有效性.     

Sequential LMI approach for the design of a BMI‐based robust observer state feedback controller with nonlinear uncertainties

This paper aims at developing a robust observer–based estimated state feedback control design method for an uncertain dynamical system that can be represented as a linear time‐invariant system connected with an integral quadratic constraint–type nonlinear uncertainty. Traditionally, in existing design methodologies, a convex semidefinite constraint is obtained at the cost of conservatism and unrealistic assumptions. This paper avoids such assumptions and formulates, the design of the robust observer state feedback controller as the feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP‐hard problem in general. The applicability of a linearization method, such as the variable change method and the congruence transformation, depends on the specific structure of the problem at hand and cannot be generalized. This paper transforms the feasibility analysis of the BMI constraint into an eigenvalue problem and applies the convex‐concave–based sequential linear matrix inequality optimization method to search for a feasible solution. Furthermore, an augmentation of the sequential linear matrix inequality algorithm to improve its numerical stability is presented. In the application part, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real‐world estimated state feedback control design problem and the necessity of the augmentation for numerical stability.     

基于观测器的鲁棒模型预测控制算法

对于含有未建模动态的输入受限离散时间线性系统,当系统状态不可测时,提出一种基于状态观测器的鲁棒模型预测控制算法。该算法采用双模型控制结构,将不变椭圆集同时应用于估计状态方程和误差方程,保证算法的稳定性和可行性,并同时给出系统稳定和可行的条件。     

基于动态参考规划的鲁棒Tube模型预测跟踪控制

为实现扰动和约束作用下对系统的最优鲁棒跟踪, 提出一种动态参考规划(DRP)方法, 设计鲁棒Tube模型预测控制器(RTMPC)将系统状态驱动到以最优跟踪点为中心的扰动不变集内. 基于DRP的RTMPC控制方法, 以多步参考为决策变量, 确保在线优化递归可行性的同时, 增加在线优化的自由度; 另外, 通过设定目标函数惩罚标称状态轨迹和参考稳态之间、以及最后一步参考稳态和设定点之间的加权欧式距离, 可实现最优鲁棒跟踪.     

Controlled invariant feasibility — A general approach to enforcing strong feasibility in MPC applied to move-blocking

Strong feasibility of MPC problems is usually enforced by constraining the state at the final prediction step to a controlled invariant set. However, such terminal constraints fail to enforce strong feasibility in a rich class of MPC problems, for example when employing move-blocking. In this paper a generalized, least restrictive approach for enforcing strong feasibility of MPC problems is proposed and applied to move-blocking MPC. The approach hinges on the novel concept of controlled invariant feasibility. Instead of a terminal constraint, the state of an earlier prediction step is constrained to a controlled invariant feasible set. Controlled invariant feasibility is a generalization of controlled invariance. The convergence of well-known approaches for determining maximum controlled invariant sets, and j-step admissible sets, is formally proved. Thus an algorithm for rigorously approximating maximum controlled invariant feasible sets is developed for situations where the exact maximum cannot be determined.     

自抗扰控制和高频信号注入的内嵌式永磁同步电机无位置传感器控制

针对内嵌式永磁同步电机无位置传感器控制系统,基于自抗扰控制技术和高频信号注入技术,提出了以转子位置角为扩张状态观测器(extended state observer,ESO)主体变量的自抗扰控制系统.该方法避免了传统算法中以电流为ESO主体变量时依靠角速度估计值积分来获得转子位置角估计值所带来的误差积累问题.该方法在电机起动、负载突变等电流波形正弦度较差的情况下,仍能保证转子位置角的估计值具有较高的精度.仿真结果验证了所提出方法的正确性和优越性.     

Stability analysis of bilinear systems under aperiodic sampled-data control

This note considers the problem of local stability of bilinear systems with aperiodic sampled-data linear state feedback control. The sampling intervals are time-varying and upper bounded. It is shown that the feasibility of some linear matrix inequalities (LMIs), implies the local asymptotic stability of the sampled-data system in an ellipsoidal region containing the equilibrium. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of numerical examples.     

持续有界扰动系统的嵌套不变椭圆集鲁棒控制

为了抑制外部持续有界扰动和模型不确定性对系统稳定性控制的影响,通过不变集理论,采用嵌套不变椭圆集鲁棒控制算法实现系统的快速稳定控制。控制算法分为离线算法和在线算法两部分。离线时根据公式得到一维状态变量序列,通过线性矩阵不等式方法优化得到嵌套不变椭圆集。在线时,根据系统状态变量在嵌套不变椭圆集的位置,构建新的不变椭圆集并计算得到系统的控制律。给出新的不变椭圆集满足系统控制要求的理论证明。通过与不变单椭圆集控制算法进行仿真比较,结果验证了上述算法的有效性,为持续有界扰动下模型不确定性系统的稳定控制,提供一种有效的控制方法。     

Computation of invariant zeros of linear,time-invariant,multivariable systems

In this paper a numerical method is presented for computing the invariant zeros of a controllable linear, time-invariant, multivariable system described by the 4-tuplo (A, B, C, D) or the triple (A, B, C). The method is based on the fact. that a controllable system can be made maximally unobservable by means of state variable feedback, thereby causing the cancellation of the invariant zeros by an equal number of the system poles. The invariant zeros are obtained as the eigenvalues of a matrix of the same dimension as the number of invariant zeros. The method is applicable to both multivariable as well as single-input, single-output systems. Examples are given to illustrate the use of the method.     

基于鲁棒一步集的Tube不变集鲁棒模型预测控制

针对一类干扰有界的输入和状态受约束线性离散系统,提出了一种基于鲁棒一步集的Tube不 变集鲁棒模型预测控制方法.首先采用多面体不变集离线设计方法得到基于多面体不变集序列的扩 展终端约束集;然后为了扩大鲁棒模型预测控制的初始状态允许区域,并提高系统的鲁棒性,在扩展终端约束集的基础上,通过引入鲁棒一步集并借助Tube不变集控制策略,设计了基于鲁棒一步集的鲁棒模型预测控制方法,并给出了算法的存在性和稳定性证明. 该方法不仅极大地扩大了初始状态允许区域,而且对有界干扰具有有效的抑制作用,使得受扰系统收敛到以原点为中心的最小鲁棒正不变集内.最后仿真验证了算法的有效性.     

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non-additive unknown disturbance

This paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed-loop input-to-state stability and recursive feasibility of the optimization problem for any piece-wise constant setpoint and non-additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.