具有多滞后非线性定常关联控制系统的镇定性研究

建立了多组多滞后定常非线性控制系统的结构 概念,采用李雅普诺夫函数分解等价法,由 Riccati矩阵微分方程的对称正定解矩阵构造正 定二次型Ｖ函数,给出了无滞后无扰动参数线性定常控制孤立子系统的镇定性,蕴含具有滞 后控制向量函数的扰动结构参数的多组多滞后区间系数定常非线性关联控制系统的关联鲁棒 镇定的一个充分条件,同时给出了扰动参数与滞后非线性项界线的估计公式．     

网络控制系统随机稳定性研究

研究了具有随机网络诱导时延及数据包丢失的网络控制系统随机稳定性问题. 本文用一个具有两个状态的马尔可夫链来描述数据通过网络传输时随机数据包丢失过程, 利用马尔可夫跳变线性系统理论, 将网络控制系统建模为一个具有两种运行模式的马尔可夫跳变线性系统, 给出了在状态反馈控制下网络控制系统随机稳定的线性矩阵不等式形式的充分条件, 最后用一个仿真示例验证了该方法的有效性.     

比例型T-S模糊控制系统稳定性分析与设计

讨论了比例型T-S模糊控制系统(TSS)的稳定性与设计问题. 利用具有乘积可换性状态矩阵的T-S系统的公共P阵构造方法及鲁棒稳定域条件, 给出了TSS系统的满足全局Lyapunov稳定的正定矩阵P的递推求解方法, 并提出一种TSS模糊控制系统设计和稳定性分析的规范化方法.     

一类不确定网络控制系统的鲁棒容错控制

研究了含有数据包丢失的不确定网络控制系统的鲁棒容错控制问题. 在执行器连续增益故障下,考虑前向网络通道和后向网络通道中存在满足马尔可夫性质的数据包丢失情况,将含有结构不确定性的闭环故障网络控制系统建模为马尔可夫跳变线性系统.基于这个模型,利用Lyapunov稳定性理论和矩阵不等式技术,给出了闭环故障系统随机稳定的充分条件,同时采用锥补线性化方法,给出了控制器设计方法.最后数例仿真验证了该设计方法的有效性.     

不确定时变线性系统的鲁棒一致渐近稳定的扰动界

不确定时变线性系统的鲁棒一致渐近稳定的扰动界奚宏生（中国科学技术大学自动化系合肥２３００２６）关键词不确定时变线性系统,鲁棒一致渐近稳定,奇异值．ｌ引言在文献［１—３］中利用状态空间方法研究了结构不确定定常线性系统参数扰动的稳定区域．本文利用时变矩阵...     

网络控制系统优化设计研究

研究网络控制系统的优化问题,提高系统的实时性。针对传统的网络控制系统是闭环系统,网络带宽有限,网络传输中的时间延迟、数据包丢失等问题不可避免。当发生以上情况时,反馈信号不能及时传回,造成控制信号发出延迟,影响了系统的实时性。为了解决上述问题,提出了一种非规律时滞补偿算法,把时滞信号引入自由权矩阵,能够得到延迟信号相关稳定性条件,并充分运用线性信号特征矩阵保证网络控制系统的性能,保证系统在线控制的实时性。证明改进方法能够避免控制信号延迟造成的滞后问题,提高了网络控制系统的实时性。     

一类随机时延网络化控制系统的容错控制研究

将一类具有随机时延的网络化控制系统建模为具有马尔可夫延迟特性的离散跳变线性系统．借助跳变线性系统理论和容错控制的思想，研究了随机时延网络化控制系统的执行器失效问题．仿真结果验证了所提方法的有效性．     

网络化系统的状态反馈保性能控制

研究了具有随机网络诱导时延且数据包丢失服从马尔可夫链的网络化系统的保性能控制问题．将网络化控制系统建模为具有两种运行模式的马尔可夫跳变线性系统．根据马尔可夫跳变线性系统理论，给出了网络化系统状态反馈保性能控制器存在的充分条件；该保性能控制器为一组线性矩阵不等式的解．通过一个仿真示例说明了本文所提方法的有效性．     

有滞后的中立型控制系统与无滞后控制系统在镇定理论中的等价性

本文对有滞后的中立型控制系统与无滞后控制系统在镇定理论中的等价性进行了讨论,用不等式估值方法及分析技巧给出了其等价的时滞范围,为简化相应的中立型控制系统的分析和设计提供了理论依据.     

多组时滞大型控制系统的镇定

给出了由无时滞线性定常闭孤立控制子系统的渐近稳定性推出多组时滞线性定常闭环大型控制系统的渐近稳定性的充分条件，并说明了所得结果可以推广到多组时滞线性时变闭环大型控制系统与多组时滞线中立型定常（或时变）闭环大型控制系统，所得结果改进了前人的结果，通过参数镇定域的比较知，可使参数镇定域扩大为原来的６倍。     

线性时滞系统的无源控制

研究一类线性时滞系统通过线性无记忆状态反馈控制律的无源控制问题。通过某个Ｒｉｃｃａｔｉ矩阵方程对称正定解的存在性,给出了使得闭环系统严格无源的控制器存在条件。进而,利用这个方程的正定解给出了无源化控制器的一个构造方法。     

多组多滞后中立型线性时变关联控制系统的结构与关联镇定

建立了具有扰动参数的多组多滞后中立型线性时变关联控制系统的结构与关联镇定新概念，采用李雅普诺夫函数鲁棒镇定等价法，给出了由无滞后无扰动参数线性时变控制系统的关联镇定，蕴含了具有扰动结构参数的多组多不足后中立型线性时变关联控制系统的关联镇定的充分性判据，同时给出了扰动参数与滞后项界限的估计公式。     

Robust stabilization of linear systems with norm-bounded time-varying uncertainty

In this paper, robust stabilization of a class of linear systems with norm-bounded time-varying uncertainties is considered. It is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a (parameter-dependent) Riccati equation. Also, a construction for the stabilizing feedback law is given in terms of the solution to the Riccati equation.     

Control of slowly-varying linear systems

State feedback control of slowly varying linear continuous-time and discrete-time systems with bounded coefficient matrices is studied in terms of the frozen-time approach. This study centers on pointwise stabilizable systems. These are systems for which there exists a state feedback gain matrix placing the frozen-time closed-loop eigenvalues to the left of a line Re s=-γ<0 in the complex plane (or within a disk of radius ρ<1 in the discrete-time case). It is shown that if the entries of a pointwise stabilizing feedback gain matrix ar continuously differentiable functions of the entries of the system coefficient matrices, then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small. It is also shown that for pointwise stabilizable systems with a sufficiently slow rate of time variation in the system coefficients, a stabilizing feedback gain matrix can be computed from the positive definite solution of a frozen-time algebraic Riccati equation     

Criterion for the convergence of the solution of the Riccati differential equation

The optimal control problem for a linear system with a quadratic cost function leads to the matrix Riccati differential equation. The convergence of the solution of this equation for increasing time interval is investigated as a function of the final state penalty matrix. A necessary and sufficient condition for convergence is derived for stabilizable systems, even if the output in the cost function is not detectable. An algorithm is developed to determine the limiting value of the solution, which is one of the symmetric positive semidefinite solutions of the algebraic Riccati equation. Examples for convergence and nonconvergence are given. A discussion is also included of the convergence properties of the solution of the Riccati differential equation to any real symmetric (not necessarily positive semidefinite) solution of the algebraic Riccati equation.     

Sensitivity of the Performance of Optimal Linear Control Systems to Parameter Variations†

The sensitivity of the index of performance to parameter variations in optimal control systems is examined in this paper. It is shown, in the case of linear optimal systems with quadratic performance criteria, that the value of the performance index, after the system parameters have deviated from a nominal set of values, is still given by a symmetric positive definite quadratic form of the initial state. The matrix of this quadratic form is governed by a special case of the matrix Riccati equation. It is shown also, that similar results hold for the performance index sensitivity function.

Because the sensitivity problem closely parallels the original optimization problem, the computational techniques used in the design of the optimal system may be reapplied in the sensitivity analysis.     

乘性随机离散系统的最优控制

基于对系统随机不确定因素的分析,文中定义了一种新型随机离散系统--乘性随机离散系统,并研究该类系统的线性二次型(LQ)最优控制问题.首先给出了该类系统的有限时间和无限时间LQ最优控制律,并着重分析、证明了无限时间LQ最优控制问题的Riccati方程的正定矩阵解的存在性及相应数值求解算法与收敛性,以及闭环系统的稳定性等问题.仿真结果表明了该方法的有效性.     

Solving the Matrix Differential Riccati Equation: A Lyapunov Equation Approach

In this technical note, we investigate a solution of the matrix differential Riccati equation that plays an important role in the linear quadratic optimal control problem. Unlike many methods in the literature, the approach that we propose employs the negative definite anti-stabilizing solution of the matrix algebraic Riccati equation and the solution of the matrix differential Lyapunov equation. An illustrative numerical example is provided to show the efficiency of our approach.      

Gain margin and Lyapunov analysis of discrete-time network synchronization via Riccati design

This paper deals with solution analysis and gain margin analysis of a modified algebraic Riccati matrix equation, and the Lyapunov analysis for discrete-time network synchronization with directed graph topologies. First, the structure of the solution to the Riccati equation associated with a single-input controllable system is analyzed. The solution matrix entries are represented using unknown closed-loop pole variables that are solved via a system of scalar quadratic equations. Then, the gain margin is studied for the modified Riccati equation for both multi-input and single-input systems. A disc gain margin in the complex plane is obtained using the solution matrix. Finally, the feasibility of the Riccati design for the discrete-time network synchronization with general directed graphs is solved via the Lyapunov analysis approach and the gain margin approach, respectively. In the design, a network Lyapunov function is constructed using the Kronecker product of two positive definite matrices: one is the graph positive definite matrix solved from a graph Lyapunov matrix inequality involving the graph Laplacian matrix; the other is the dynamical positive definite matrix solved from the modified Riccati equation. The synchronizing conditions are obtained for the two Riccati design approaches, respectively.     

Optimization of formation for multi-agent systems based on LQR

In this paper, three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator (LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost, because both the collective object (such as formation or consensus) and the individual goal of each agent are very important for the overall system. First, we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings. The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation (ARE). It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix. Next, for physically interconnected multi-agent systems, the optimal formation algorithm is presented, and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown. Finally, if the communication topology between agents is fixed, the local feedback gain is obtained from the solution to a quadratic equation with one unknown. The equation is derived from the derivative of the cost function with respect to the local feedback gain. Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.