一种模型参考鲁棒控制的跟踪性能改善

This paper considers the tracking performance problem of a model reference robust control (MRRC) for plants with relative degree greater than one. A new algorithm is proposed based on the earlier research. It is shown that by applying a special transformation to the tracking system, the L1 bound of the tracking error can be achieved even when the high frequency gain is unknown, and both the tracking performance and the control effort can be improved significantly. Furthermore, the strictly positive real (SPR) condition, which is an essential assumption of the earlier design, can be removed.     

参数不确定离散广义大系统的保性能控制

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper. The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model. The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities (LMIs), and a desired state feedback controller is obtained via convex optimization. An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

线性二次闭环微分对策次优对策的双线性矩阵不等式方法

The suboptimal control program via memoryless state feedback strategies for LQ differential games with multiple players is studied in this paper. Sufficient conditions for the existence of the suboptimal strategies for LQ differential games are presented. It is shown that the suboptimal strategies of LQ differential games are associated with a coupled algebraic Riccati inequality. Furthermore, the problem of designing suboptimal strategies is considered. A non-convex optimization problem with BMI constrains is formulated to design the suboptimal strategies which minimizes the performance indices of the closed-loop LQ differential games and can be solved by using LMI Toolbox of MATLAB. An example is given to illustrate the proposed results.     

非线性互联大系统的最优控制:逐次逼近法

The optimal control problem for nonlinear interconnected large-scale dynamic systems is considered. A successive approximation approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling, nonlinear two-point boundary value (TPBV) problem is transformed into a sequence of linear decoupling TPBV problems. It is proven that the TPBV problem sequence uniformly converges to the optimal control for nonlinear interconnected large-scale systems. A suboptimal control law is obtained by using a finite iterative result of the optimal control sequence.     

离散线性时滞系统的次优控制:逐次逼近法

A successive approximation approach for designing optimal controllers is presented for discrete linear time-delay systems with a quadratic performance index. By using the successive approximation approach, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems without time-delay and time-advance terms. The optimal control law obtained consists of an accurate feedback terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint equations. By using a finite-step iteration of the time-delay compensation term of the optimal solution sequence, a suboptimal control law is obtained. Simulation examples are employed to test the validity of the proposed approach.     

基于LMI技术的两个神经元的时滞混沌神经网络的耦合延迟同步研究

In this paper, the chaotic lag synchronization of coupled time-delayed systems with two neurons is investigated. We analyze the asymptotic stability for the error dynamical system based on Lyapunov method and linear matrix inequality (LMI) technique. Some new sufficient conditions for determining the lag synchronization between the coupling systems are derived. Above all, we skillfully shift our criterion which is expressed in terms of LMI into the generalized eigenvalue minimization programming (GEVP) for the first time. The minimum of coupling strength is obtained successfully. A numerical experiment illustrates the effectiveness and advantage of our results.     

脉冲时滞微分不等式及鲁棒控制设计中的应用

本文首先建立脉冲微分不等式的稳定性结果。利用此结果并结合Ｒｉｃｃａｔｉ方程方法,对含变时滞测度微分系统给出了其鲁棒控制设计,最后给出一设计实例。     

输入约束系统的滚动时域输出反馈控制方法研究

This paper addresses the H∞ output feedback control problem for discrete-time systems with actuator saturation. Initially, a constrained H∞ output feedback control approach is presented in the framework of linear matrix inequalities (LMI) optimization. Under certain assumptions on the disturbance energy bound, closed-loop H∞ performance is achieved. Furthermore, the moving horizon strategy is applied to an online management of the control performance so that the closed-loop system can satisfy control constraints in the case of unexpected large disturbances. A dissipation constraint is derived to achieve the moving horizon closed-loop system dissipative. Simulation results show that the constrained H∞ controller works effectively under the disturbance assumption and that the moving horizon H∞ controller can trade-off automatically between satisfying control constraints and enhancing performance.     

基于H∞/H2的多变量约束热轧带钢AGC鲁棒控制

研究了热轧带钢自动厚度控制(AGC)的鲁棒控制问题.为了消除轧制过程中其它变量对厚度控制精度的影响,提出了一种基于H∞/H2的多变量约束控制策略.首先,采用高阶未建模扰动对控制输入传函的H∞范数作为鲁棒性能指标,张力与活套等约束量对输出评价信号传函的H2范数作为LQG性能指标,建立了受约束的厚度控制模型.其次,设计了H∞/H2状态反馈鲁棒控制器,把受约束的AGC控制转化为系统在模型摄动与外界扰动下满足一定性能指标的鲁棒控制问题.最后,仿真结果表明,所设计的H∞/H2控制器具有良好的鲁棒控制特性.     

谱约束下反对称正交反对称矩阵束的最佳逼近

东莞理工学院软件学院,广东东莞523808矩阵逆特征值问题的研究已有一些很好的成果,但对矩阵广义逆特征值问题的研究还不多见,本文讨论了反对称正交反对称矩阵的广义逆特征值问题,丰富了矩阵理论和方法,得到了通解和最佳逼近解,并给出了数值例子.     

Matrix Approximation with Constraints of Matrix Inequalities and Applications in Robust Control

This paper deals with a general class of optimization problems in robust control with given expectation value of performance index,which can be transformed into the problem of matrix approximation with matrix inequalities constraints.Theorem for existence and the uniqueness of the solutions of matrix approximation with linear matrix inequalities (LMIs) constraints is presented and algorithms for solving the problems of matrix approximation with matrix inequalities constraints are given based on the fact that such problems can be converted into the generalized eigenvalue problem (GEVP) of LMI.Examples are given to illustrate the main results of the paper.     

基于区域极点约束的鲁棒H2控制

考虑了在区域极点约束下状态反馈的鲁棒H2控制问题.分别对含多面体不确定性的连续和离散系统进行了讨论.基于LMI,给出了存在参数相关的Lyapunov矩阵的充分条件.利用LMI凸优化方法的解,所得静态反馈控制器,不仅保证闭环系统的极点在-给定区域内,而且还使性能指标H2的一上界达到最小.     

Robust stabilization for systems with rank-one uncertainty structure

This paper solves a class of robust control problems, with output feedback, for systems with mixed parametric uncertainty and unmodeled dynamics. This class of problems is characterized by a special rank-one assumption on the transfer matrix of the nominal plant. Under this assumption, the robust stabilization problem is reduced to a convex feasibility problem involving linear matrix inequalities. The data necessary to assemble these inequalities can be readily obtained from a state-space model of the nominal plant.     

饱和约束系统的鲁棒模型预测控制

针对饱和约束系统提出了一种鲁棒模型预测控制算法,分别考虑了多面体不确定性和结构反馈不确定性.考虑无穷时域的最坏二次性能指标,通过采用带有饱和特性的反馈控制结构,将控制律的求解转化为一个在线的线性矩阵不等式优化问题.初始时刻优化问题的可行性保证了闭环控制系统的鲁棒稳定性.最后的仿真结果说明了算法的优越性.     

一类随机摄动系统的鲁棒控制与仿真

在内模控制(IMC)结构下对一类随机摄动系统的鲁棒控制及其仿真研究作了探讨.首先针对一类随机模型误差的描述定义了一个实际敏感度和标称敏感度之间的加权敏感度误差,然后应用谱分解的方法调整标称控制器来最小化加权敏感度误差在整个频段上的方差,为一类随机摄动系统提供了一种鲁棒控制器设计方法,可使系统期望的标称性能对模型误差具有良好的鲁棒性.最后根据随机摄动系统的特点进行仿真研究,进一步说明了所得控制方法的有效性.     

基于线性矩阵不等式的Acrobot鲁棒镇定控制

针对欠驱动机器人Acrobot,提出一种基于线性矩阵不等式的鲁棒镇定控制方法。通过将Acrobot在垂直向上不稳定平衡点附近的第一杆角速度看作一种不确定性,得到Acrobot的不确定模型,在此基础上设计一种基于线性矩阵不等式的鲁棒镇定状态反馈控制律,实现Acrobot较大范围的平衡控制。仿真和对比结果验证了方法的有效性和优越性。     

Periodically Time‐Varying Memory State‐Feedback for Robust H2 Control of Uncertain Discrete‐Time Linear Systems

This study is concerned with the synthesis of periodically time‐varying memory state‐feedback controllers (PTVMSFCs) for discrete‐time linear systems. In our preceding studies, we have already established a solid theoretical basis for linear matrix inequality (LMI)‐based (robust) H _∞‐PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H ₂ performance criterion. In the H ₂ case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and the inequalities for bounding traces that characterize the H ₂ norm. We can overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H ₂‐PTVMSFC synthesis. On the basis of this result, we also consider robust H ₂‐PTVMSFC synthesis for LTI systems with parametric uncertainties.     

Robust Input Covariance Constraint Control for Uncertain Polytopic Systems

In this paper, the robust input covariance constraint (ICC) control problem with polytopic uncertainty is solved using convex optimization with linear matrix inequality (LMI) approach. The ICC control problem is an optimal control problem that optimizes the output performance subjected to multiple constraints on the input covariance matrices. This control problem has significant practical implications when hard constraints need to be satisfied on control actuators. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the robust ICC control problem for polytopic uncertain systems. Both continuous‐ and discrete‐time systems are considered. Parameter‐dependent and independent Lyapunov functions have been used for robust ICC controller synthesis. Numerical design examples are presented to illustrate the effectiveness of the proposed approach.     

时变不确定性关联系统的分散鲁棒稳定控制器设计

对一类满足匹配条件的时变不确定性关联大系统,给出了其可分散状态反馈镇定的充分条件即一组线性矩不等式（ＬＭＩ）有解,在此基础上,通过求解一凸优化问题,指出了具有较小反馈益的分散稳定化状态反馈控制律的设计方法,文中的仿真示例说明了该方法的有铲笥和优越性。     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints. A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function. At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method. A numerical example is given to illustrate the main results.