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．     

区域极点约束下线性离散系统的Riccati鲁棒控制

讨论区域极点约束下,含结构参数扰动的不确定线性离散系统的鲁棒控制问题,即设计一 鲁棒状态反馈控制器,使线性离散系统在可允许的参数扰动下,闭环矩阵极点始终位于一预先 给定的圆形区域中,从而闭环系统具有期望的动态性能.上述控制目的可通过求解一含参数 的代数离散Riccati方程达到.     

A study of robust controller and observer design method for a rolling object and beam system

This paper deals with a robust control problem for a ball and beam system with an uncertainty. At first, we clarify the effect of a measurement error in the beam rotational angle and its differential value. It is expressed as additional terms in the state and input matrix of the state equation, which is called as a structured uncertainty. For this system, a robust tracking controller and a robust state observer are applied. Both components are designed based on a robust control, which is called guaranteed cost control. This is a kind of cost minimization method for designing problem of a linear feedback system. The controller is obtained as the solution of the matrix algebraic Riccati like equation, which is referred to as stochastic algebraic Riccati equation. The nominal system performance is degraded due to the influence of the uncertainty, but it is able to design a system with robustness for disturbance. Next, we consider the design problem of a state observer to estimate all state variables form the output signal easy to measure, like rotation angle of the beam. For the design problem of the state observer, we consider dual problem of the original system. Consequently, our proposed system estimates the whole state vector, and using estimated state values, it controls the ball to the desired position. Both components have robustness for the uncertainty. Numerical result shows the validity of our proposed method.     

具有参数不确定性和外干扰系统的鲁棒H-状态反馈控制

本文考虑具有参数不确定性和外干扰系统的鲁棒Ｈ∞状态反馈控制问题。这个问题的解只需求解一个代数Ｒｉｃｃａｔｉ方程就可得到其状态反馈阵，且这个状态反馈阵仍保持和ＬＱ最优设计相同的形式。运用这样的状态反馈控制。即能保证具有参数不确定性系统是稳定的，又能达到Ｈ∞最优干扰抑制效果。     

The piecewise parametric optimal control of uncertain linear quadratic models

The optimal control of linear quadratic model is given in a feedback form and determined by the solution of a Riccati equation. However, the control-related Riccati equation usually cannot be solved analytically such that the form of optimal control will become more complex. In this paper, we consider a piecewise parametric optimal control problem of uncertain linear quadratic model for simplifying the form of optimal control. By introducing a piecewise control parameter, a piecewise parametric optimal control model is established. Then we present a parametric optimisation method for solving the optimal piecewise control parameter. Finally, an uncertain inventory-promotion optimal control problem is discussed and a comparison is made to show the effectiveness of proposed piecewise parametric optimal control model.     

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.     

High-gain observer approach to disturbance attenuation using measurement feedback

A procedure is developed for disturbance attenuation in a linear system via the use of measurement feedback. A high-gain observer is used to recover the disturbance attenuation properties asymptotically, which can be achieved using full state feedback. It is thus shown that the problem of disturbance attenuation via measurement feedback can be decomposed into two problems of disturbance attenuation via state feedback. These problems of disturbance via state feedback can then be solved using existing methods based on the algebraic Riccati equation.     

具有对称循环结构的大系统Riccati方程的求解

本文研究了具有对称循环结构的大系统的代数Ｒｉｃｃａｔｉ方程和Ｌｙａｐｕｎｏｖ矩阵方程的求解问题，结果表明，这类系统的代数Ｒｉｃｃａｔｉ方程和Ｌｙｐａｐｕｎｏｖ矩阵方程的求解问题可以简化为求解Ｎ／２＋１个独立的低阶方程，做为一个应用，这类系统的二次型最优控制问题和鲁棒二次型最优控制问题也可以简化。     

LQ最优控制系统中加权阵的确定

本文研究了LQ最优调节器的逆问题.在控制变量加权矩阵R给定的条件下,通过引入 一组自由变量,给出了满足闭环系统特征值要求的状态加权矩阵Q的一种参数化表示结果.基 于这种结果,研究了LQ逆问题的矩阵变换解法和一类系统的LQ逆问题的解法.此外,文中 还给出了不求解代数矩阵Riccati方程确定系统的最优状态反馈系数矩阵K的方法.     

弓网接触力反馈线性化控制

通过扩展状态变量得到受电弓的非线性模型,利用非线性系统的微分几何理论,构造微分同胚变换和状态反馈表达式,得到了受电弓线性化模型,设计反馈控制律解决弓网接触力的跟踪问题,并证明了内状态的一致最终有界性,考虑弓头易受干扰问题,采用非线性干扰观测器补偿反馈控制律.研究对比表明,所提出的基于干扰观测器的反馈线性化控制策略能有效解决弓网接触力的跟踪问题,同时克服了反馈线性化控制依赖于精确模型的缺点,为一定工况下弓网最优接触力的跟踪控制提供可行方案.     

一类不确定动态时滞系统的无记忆鲁棒镇定控制

针对状态和控制均存在滞后,同时具有未知且有界的一类时变不确定线性时滞系 统,提出了一种无记忆鲁棒镇定控制器设计算法.给出了闭环系统二次稳定的充分条件,并利 用一等价线性时不变系统的H∞标准问题综合方法来构造出所需的线性状态反馈控制律,即 可通过求解一代数Riccati型方程来求得控制律静态增益阵,从而保证了解的存在性和可解 性.     

Optimal control for a polynomial system with a quadratic criterion over infinite horizon

This paper proposes an optimal control algorithm for a polynomial system with a quadratic criterion over infinite horizon. The designed regulator gives a closed-form solution to the infinite horizon optimal control problem for a polynomial system with a quadratic criterion. The obtained solution consists of a feedback control law obtained by solving a Riccati algebraic equation dependent on the state. Numerical simulations in the example show advantages of the developed algorithm.     

受扰线性离散系统的前馈2反馈最优控制

研究具有已知动态特性但未知初始条件的持续外界扰动的线性离散系统最优控制问题。给出了前馈一反馈最优控制律的存在唯一性条件，并提出了最优控制律的设计算法．通过降维扰动观测器解决了前馈一反馈最优控制律的物理不可实现问题．对近海结构物振动控制的实例仿真表明，该设计算法易于实现，在抑制外部持续扰动和鲁棒性方面优于经典的状态反馈最优控制。     

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     

一种鲁棒故障检测与反馈控制的最优集成设计方法

研究线性不确定系统的反馈控制器与鲁棒故障检测滤波器集成设计问题.基于新提出 的性能指标函数,将鲁棒故障检测滤波器设计问题归结为最优化问题,通过求解Riccati方程可 得到鲁棒故障检测滤波器设计问题的最优解.在共用同一状态观测器的情况下,将反馈控制器 和鲁棒故障检测滤波器的集成设计问题归结为两目标优化问题,解决了同时满足闭环控制系统 设计要求和故障诊断系统鲁棒性能的最优集成设计问题.简例验证了提出算法的有效性.     

具有状态滞后的线性不确定时滞系统鲁棒输出反馈控制(英)

针对具有状态滞后和时变未知且有界不确定性的线性时变不确定时滞系统，研究了当状态不完全可测时的鲁棒镇定问题．利用Riccati方程方法，提出了一种基于观测器的动态输出反馈镇定控制器设计方法，并得到了不确定时滞系统可输出反馈镇定的充分条件．最后通过一数值例子来说明了所得结果的可行性．     

具有指定闭环特征值的离散时间最优调节器的设计

本文研究了LQ最优调节器的逆问题。在控制变量加权矩阵R给定的条件下,通过引入一组自由变量,给出了满足闭环系统特征值要求的状态加权矩阵Q的一种参数化表示结果。基于这一结果,文中研究了一类系统的LQ最优调节器之逆问题的解析解法。通过所求得的自由变量解,就可以直接确定系统的最优状态反馈控制器。     

Optimal Output Feedback Controllers for Spacecraft Attitude Tracking

This paper investigates the problem of output feedback attitude tracking control of a rigid spacecraft in the presence of external disturbances. Two optimal control laws with a disturbance estimator are developed to deal with this problem. An adapted extended state observer is used to estimate the angular velocity tracking errors and to allow for compensation for the total disturbances. The proposed control can be expressed as the sum of a nonlinear optimal controller and an estimated disturbance. For the optimal controller, the state‐dependent Riccati equation and optimal Lyapunov techniques are employed to solve the infinite‐time nonlinear optimal control problem. The developed controllers can minimize a performance index and ensure the stability of the closed‐loop system and external disturbance attenuation. On the other hand, using the adapted extended state observer, the asymptotic convergence of estimation error dynamics is proven. An example of multiaxial attitude manoeuvres is given and simulation results are included to demonstrate and verify the usefulness of the proposed controllers.     

一类不确定非线性系统的鲁棒H∞控制

讨论了在自由系统和输入通道都带有有界不确定性的仿射非线性系统的鲁棒H∞ 控制问题,给出了状态反馈控制设计,对所有允许的不确定性它既能保证关于H∞模的干扰 抑制品质,又能镇定该系统.同时指出如果一个相应的Hamilton-Jacobi不等式有非负解,则 该不确定仿射非线性系统的鲁棒H∞控制问题可解.