广义二阶动力学系统的鲁棒特征结构配置

考虑了具有摄动的广义二阶动力学系统的鲁棒特征结构配置问题, 提出了一种优化算法. 该算法的目标是使得特征结构配置的误差最小. 根据广义二阶动力学系统基于状态加微分反馈的参数化特征结构配置结果, 给出了优化指标的完全参数形式. 该算法不包含“返回”过程, 允许特征值在一定范围内参与优化, 能够给出鲁棒性较强的控制系统. 数值例子说明了算法的有效性.     

鲁棒比例与部分状态导数反馈控制系统设计

基于广义线性系统比例与部分状态导数反馈参数化特征结构配置结果和矩阵对广义特征值灵敏度结果, 得到了关于开环系统矩阵中摄动元素的闭环特征值灵敏度的参数表达式, 并在此基础上提出了广义线性系统比例与部分状态导数反馈最小灵敏度特征值配置的有效算法. 该算法不含有"返回"过程, 允许闭环特征值在希望的区域内方便地参与优化. 一个算例说明了算法的简单性和有效性.     

矩阵二阶系统的鲁棒极点配置

直接在矩阵二阶框架下,利用特征结构配置参数化方法,研究矩阵二阶线性系统的鲁棒极点配置问题.将两种测量闭环特征值灵敏度方法有机地结合起来,给出一个新的优化性能指标,此指标的优化过程完全依赖于特征结构配置中的设计自由度.为进一步提高闭环系统的鲁棒稳定性,闭环极点也作为设计自由度的一部分参与优化.数值例子分析结果表明了该方法的有效性.     

可重构飞行控制律设计的混合特征结构配置方法研究

将特征结构配置与模糊控制理论相结合对飞机侧向飞行重构控制律进行设计.首先介绍了重构控制律中特征结构配置的原理和反馈增益矩阵的算法实现,在此基础上结合带优化修正参数的无量化模糊控制方法对闭环系统进行鲁棒控制器设计.该控制策略以特征结构配置作为故障后系统的内环控制器,模糊控制器作为外环控制器,使系统获得较好的动态性能和较强的鲁棒性.仿真结果表明系统有效抑制了内部参数摄动对飞行任务的不良影响.     

基于在线优化的线性系统状态反馈鲁棒镇定

建立关于Sylvester方程的鲁棒极点配置梯度流优化算法模型,在线求解相应的二次优化问题,并在线计算状态反馈增益矩阵.使得闭环系统矩阵的伞部特征值位于给定的区域中.对于一切满足条件的扰动,具有最小灵敏度,闭环系统人范围一致渐近稳定.仿真结果验证了该方法适用十非线性系统的鲁棒镇定问题和在线鲁棒极点配置问题.     

状态反馈极点配置问题的一种新算法

将Wonham可控规范型作了推广,给出了一种新的状态反馈极点配置问题算法,首先讨论了单输入系统情况,对多输入系统将其分解为若干个单输入系统而求解,其优点是不需要计算系统的特征多项式,介绍了该方法的基本原理、求解步骤,得到了反馈增益矩阵的一般表达式.该表达式中含有可供任意选择的参数,通过对参数的适当选取,可适应控制系统的其他性能要求.     

基于特征结构配置和直接自适应的侧向飞行控制律设计

将特征结构配置与直接自适应理论相结合对飞机侧向飞行控制律进行设计.首先介绍了特征结构配置的原理和反馈增益矩阵的算法实现,在此基础上结合直接自适应方法对闭环系统进行鲁棒控制器设计.该控制策略以特征结构配置作为内环控制器,自适应控制器作为外环控制器,使系统获得较好的动态性能和较强的鲁棒性.某飞机的侧向飞行控制律设计仿真结果表明系统获得了良好的动态性能,并且有效抑制了内部参数摄动对系统的不良影响.     

基于混合灵敏度优化的鲁棒特征结构配置

将H_∞理论的混合灵敏度指标融入到特征结构配置中, 将混合灵敏度指标转换为特征结构设计参数的函数关系, 建立了特征结构配置的频率域指标约束. 这两种方法的结合各自利用了其在时域和频率域的设计优势. 通过优化算法所获得的鲁棒特征结构配置, 既保证了闭环特征值/特征向量, 又使反馈回路具有一定的频率域特性. 计算实例表明这种综合设计方法的有效性.     

线性系统的鲁棒状态反馈控制器

本文基于线性系统的状态反馈特征结构配置结果和矩阵特征值灵敏度分析理论,提出了线性系统的一种鲁棒状态反馈控制器,它在满足闭环系统特性要求的前提下,使得闭环极点关于系统参数摄动具有最小的灵敏度.     

利用位置和加速度反馈的矩阵二阶系统特征结构配置

考虑一类利用位置和加速度反馈二阶线性系统的特征结构配置问题．在允许闭环系统的特征值是未知的前提下,结合矩阵多项式的右互质分解提出二阶线性系统特征结构配置的参数化方法,建立反馈增益阵和特征向量矩阵的显示参数化表达式．本文涉及的参数化方法直接将二阶系统模型转化为一阶状态空间形式,从而降低了系统设计中的计算工作量,并且提出的算法简单,无“返回”步骤．最后,数值算例表明了该算法的有效性．     

Eigenvalues of partitioned matrices "generated" by a matrix with known eigenvalues

A method is shown which allows to compute the eigenvalues of anmn-dimensional square matrixFfrom the eigenvalues of ann-dimensional matrixA, if the m²submatrices ofFare describable by convergent power series ofA. As an illustration, matrices arising in a multivariable feedback control system are considered.     

State feedback sliding mode control without chattering by constructing Hurwitz matrix for AUV movement

This paper presents a new method to eliminate the chattering of state feedback sliding mode control (SMC) law for the mobile control of an autonomous underwater vehicle (AUV) which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.     

Practical output tracking of nonlinear systems with uncontrollableunstable linearization

The paper focuses on the problem of having the output of nonlinear systems track a prescribed C¹ reference signal. It is proved that, under mild assumptions, global practical output tracking is achievable by smooth state feedback, although asymptotic output tracking is usually not possible (even locally) because the linearized system has uncontrollable modes whose eigenvalues are on the right half plane. Smooth feedback controllers which solve the problem of global practical output tracking are explicitly constructed, based on a modified 'adding a power integrator' approach. This feedback design method also leads to solutions to challenging benchmark control problems, including practical output tracking of an underactuated unstable two degrees of freedom mechanical system     

Stabilization of linear multivariable constant delay-differential systems

The article presents the iterative method of stabilizing control signal selection in the form of the state-feedback of a multivariable linear time-invariant plant with delays. The proposed method is based on the consecutive assignment of the single system eigenvalues λ_j so that its stabilizability will be preserved for a given iteration step and the assigned eigenvalues will not be changed, even though a dynamical element identified by the matrix K_j(z) (where z is an elementary delay operator) is placed into the state feedback. To illustrate the abovementioned method, a simplified example is given.     

Feedback stabilization of connected nonlinear oscillators with uncontrollable linearization

A nonlinear system with uncontrollable linearization is under investigation. The uncontrollable part of the linearization is assumed to have no eigenvalues in the right half-plane and have eigenvalues with zero real and nonzero imaginary part. A nonlinear feedback loop is assumed to carry out a connection between the controllable part of the system and the uncontrollable one. The control law of the controllable part is defined to be a linear function of the state variables. This linear feedback loop can maintain the stability of a whole control system provided its feedback law coefficients satisfy a system of algebraic inequalities. The consistence of this system of inequalities is proved.     

Design of sensitivity-reducing compensators using observers

In this paper the design of compensators for output feedback systems which satisfy a sensitivity, reduction criterion is considered for the case when the dynamic compensator is an observer. Using the conditions for comparison sensitivity design of output feedback systems derived by Naeije and Bosgra [4], it is shown that for arbitrary stable state-observers (full or reduced order) there exist feedback gains multiplying the system output and observer states for which the system is stable and the sensitivity reduction criterion is satisfied. Use of observers enables direct control over some of the feedback system eigenvalues and leads to a useful interpretation of the sensitivity weighting matrix. A design procedure is described and illustrated by an example of an aircraft control. The results are graphically compared with results obtained by a conventional design procedure.     

A design scheme for incomplete state or output feedback with applications to boiler and power system control

The problem of designing a linear feedback when all state variables are not available is discussed. The design scheme is based on computation of a complete state feedback and a reduction to a specified structure. The reduction is made by approximation of the eigenspace corresponding to a set of dominant eigenvalues. The method consists of successive choices of weightings on this space. The method is applied to the control of a boiler and a three-machine power system. In the power system case the complete state feedback can be replaced by local output feedback without significant decrease in performance.The examples indicate that the proposed method is a realistic design method for multivariable systems.     

具有多图拓扑结构的同类智能体LQR控制

本文考虑具有一般线性时不变动态特性的多智能体系统优化控制问题. 将智能体之间的通讯拓扑结构建模成具有自环的无向多图, 每个子系统就是一个节点, 每个节点的控制行为只与本身及邻居节点有关. 由于反馈矩阵具有块对角结构约束, 本文研究的LQR控制问题本质上是一类结构优化问题. 最小化系统LQR性能指标等价于最小化单个智能体性能指标和. 基于线性矩阵不等式得到系统的次优性能指标, 指出LQR性能域是凸集. 由此多智能体系统的LQR控制转化为若干个子系统的LQR控制, 可以通过求解系数是Laplacian矩阵最小最大特征值的两个矩阵不等式得到反馈增益. 数值例子验证了方法的有效性.     

Difference feedback can stabilize uncertain steady states

The paper is concerned with the stabilization of uncertain steady states by the state difference feedback. The feedback method has a peculiar feature that it uses only the difference between the present state x(t) and the past state x(t-T), considering exact information on the steady state is unavailable. Hitherto a condition is known under which such stabilization can not be realized. The article conversely shows that the state difference feedback can stabilize only if the exclusion condition is not true. Furthermore a dynamic output difference feedback is shown to be able to stabilize under quite a mild condition that the steady state is not associated with zero eigenvalues. The ability of the method is illustrated by using a cart-pendulum system which moves along a one dimensional varying slope     

Linear systems with bounded inputs: global stabilization with eigenvalue placement

This work presents a technique for obtaining a bounded continuous feedback control function which stabilizes a linear system in a certain region. If the open-loop system has no eigenvalues with positive real part, the region of attraction of the resulting closed-loop system is all ℝⁿ, i.e., the feedback control is a global stabilizer; otherwise, the region contains an invariant (‘cylindric-like’) set where the controller does not saturate. The proposed control is a linear-like feedback control with state-dependent gains. The gains become implicitly defined in terms of a nonlinear scalar equation. The control function coincides in an ellipsoidal neighbourhood of the origin with a linear feedback law which is a solution of a linear quadratic regulator problem. This design allows eigenvalue placement in a specified region. © 1997 by John Wiley & Sons, Ltd.