线性区间离散时滞系统的区域镇定

针对线性离散时滞系统的区域镇定问题, 基于非奇异状态变换技术提出了区间不确定性系统区域可镇定的充分条件, 保证闭环系统的所有极点均位于给定的圆盘区域内. 所给条件可简化为LMI描述形式, 利用LMI工具求解非常方便. 所给实例表明了该方法用于判断线性区间离散时滞系统的区域可镇定性与设计区域镇定控制器的可行性.     

带传输滞后的线性离散系统的状态反馈镇定

针对存在传输滞后的线性离散系统的状态反馈镇定问题,给出了系统可镇定的一个内部限制条件.为克服这一限制条件,提出了两种方法:一种是充分利用滞后状态的信息,另一种是设计带有递推动态的状态反馈控制器.研究结果表明,若系统在没有传输滞后时能通过状态反馈被镇定,则存在传输滞后时一定也能通过设计新的控制器使系统被镇定.     

基于反馈线性化的MIMO非最小相位系统指数镇定

针对仿射多输入多输出非线性非最小相位系统,提出了一种新的镇定方案.用反馈线性化解耦系统输入输出关系,通过高增益状态反馈镇定系统外部动态,用模型预测控制镇定内部动态,所设计控制器能保证闭环系统的指数稳定性.仿真结果表明了所提出方法的有效性和优越性.     

线性时滞系统滞后反馈鲁棒镇定

本文研究时不变线性时滞系统的鲁棒镇定问题。通过建立时滞系统的一个渐近稳定性定理，对摄动矩阵满足匹配条件和不满足匹配条件的情况分别给出了完全鲁棒镇定控制器的设计方法与鲁棒镇定控制器的存在性充分条件和设计方法；文中尤其提出了非滞后线性系统的一种简单的滞后反馈镇定方案。文末用例子示例了本文的设计方法。     

连续时间T-S模糊系统的一种二次镇定方法

模糊隶属函数是模糊系统的重要组成部分,在系统镇定中考虑其结构和参数信息可以减少结果的保守性.为此,针对连续时间T-S模糊系统的二次镇定问题,提出一种新的放松二次镇定条件.运用一种有效的附加变量引入方式将隶属函数乘积界这一信息更好地纳入系统的镇定条件中,得到了比以往文献保守性更小的结果.所有结果均以线性矩阵不等式形式给出.仿真结果验证了所提出方法的有效性.     

基于反馈线性化的MIMO非最小相位系统指数镇定

针对仿射多输入多输出非线性非最小相位系统,提出了一种新的镇定方案.用反馈线性化解耦系统输入输出关系,通过高增益状态反馈镇定系统外部动态,用模型预测控制镇定内部动态,所设计控制器能保证闭环系统的指数稳定性.仿真结果表明了所提出方法的有效性和优越性.

     

r 阶鲁棒稳定性与零动态非渐稳单入单出系统的静态分叉控制镇定

研究零动态非渐稳的单输入单输出控制系统的局部渐近镇定问题,讨论了对这种系统镇定的设计方法,并对一类满足条件(S)的系统,利用静态分叉控制结果,提供了构造反馈控制函数使上述系统局部渐近镇定的方法.该方法也可看作是静态分叉控制在某些情况下的一种简化.     

具有输入饱和的组合系统的分散控制

研究了一类具有饱和输入的组合系统的分散可镇定问题. 运用M-矩阵方法, 通过线性分散状态反馈得出具有饱和输入组合系统的可镇定的充分条件. 对于具有对称结构的组合系统, 给出了更为简单的镇定条件.     

欠驱动不对称船舶全局K指数镇定的解耦实现

研究一类欠驱动不对称船舶的全局K指数镇定问题,并且提出一种新的解耦控制方法.首先,对船舶系统进行全局微分同胚变换和状态时变变换,并将其解耦为线性子系统和线性时变子系统,从而将整个系统的镇定控制问题转化为两个简单子系统的镇定问题,简化了控制器的设计;然后,为每个子系统分别设计独立的全局时变指数镇定控制律,实现了欠驱动不对称船舶的全局K指数镇定;最后,仿真结果表明了所提出方法的有效性.     

离散模糊系统镇定律设计

研究离散型T-S模糊系统镇定问题.针对给出的状态空间模型,基于稳定性判定条件给出了镇定律的直接设计方法,通过求解一组线性矩阵不等式完成模糊系统镇定律的设计.给出的算例说明了该方法的有效性.     

基于非理性博弈的舆情传播仿真建模研究

随着社交网络的不断发展,借助社交网络进行传播的舆情信息的威胁越来越大. 本文利用博弈论的方法研究了舆情信息的传播机制,从理性博弈和非理性博弈的角度出发对个体与邻居的交互行为进行建模. 随后以目前较为成熟的传染病模型为基础,通过引入传播学中的社会威慑因素来构建基于非理性博弈的舆情传播模型,以实现适应舆情传播研究的仿真系统,继而将基于非理性博弈的舆情传播模型在无标度网络和小世界网络上的动力学特征进行理论分析. 在仿真环境中对非理性博弈的舆情传播模型进行实验,分析模型参数、网络密度和舆情传播源对舆情传播的影响,其结果符合理论分析结果. 最后对无标度网络上舆情传播的控制策略进行了研究,包括:社会威慑方法、目标免疫方法和正面消息方法,为社交网络上的政策制定提供了理论基础.     

Design of non-rational MIMO feedback systems with inputs and outputs satisfying certain bounding conditions by using rational approximants

When a feedback system has components described by non-rational transfer functions, a standard practice in designing such a system is to replace the non-rational functions with rational approximants and then carry out the design with the approximants by means of a method that copes with rational systems. In order to ensure that the design carried out with the approximants still provides satisfactory results for the original system, a criterion of approximation should be explicitly taken into account in the design formulation. This paper derives such a criterion for multi-input multi-output (MIMO) feedback systems whose design objective is to ensure that the absolute values of every error and every controller output components always stay within prescribed bounds whenever the inputs satisfy certain bounding conditions. The obtained criterion generalizes a known result which was derived for single-input single-output (SISO) systems; furthermore, for a given rational approximant matrix, it is expressed as a set of inequalities that can be solved in practice. Finally, a controller for a binary distillation column is designed by using the criterion in conjunction with the method of inequalities. The numerical results clearly demonstrate that the usefulness of the criterion in obtaining a design solution for the original system.     

Limiting zero distribution of sampled systems

In this paper, we consider the sampling of a continuous time system with possibly a non-rational transfer function. Limiting zero distribution of the sampled system represented by an FIR model is derived. It is shown that the zeros of the FIR sampled system converge evenly to the unit circle or to the unit disk plus unstable roots of the reciprocal polynomials depending on assumptions.     

A criterion of approximation for the method of inequalities

A criterion of approximation is derived for replacing a plant transfer function which is either non-rational or is rational but large or is not accurately known, by a convenient rational approximant for the purposes of designing a control system. The criterion provides simple sufficient conditions on the accuracy of approximation to ensure that designs carried out with the approximant are valid.     

Synthesis of non-rational controllers for linear delay systems

This paper addresses the control of linear delay systems using non-rational controllers. The structure of the controller is chosen so as to copy the structure of the plant, reproducing the delays in the state and in the output. The resulting stabilization and performance design problems are entirely expressed as linear matrix inequalities. Although the design inequalities are based on delay independent stability conditions, the overall design is delay dependent, in the sense that the controller makes use of the delay parameter of the plant. This parameter is assumed to be constant yet arbitrary. Using non-rational controllers we overcome the main difficulty faced when designing rational controllers for linear delay systems, which is to incorporate in the design problem the matrix multiplier used to prove stability with respect to the delayed part of the system. We illustrate the paper with several examples and provide extensive comparisons with existent results.     

Topological orbital equivalence with asymptotic phase for a two time-scales discrete-time system

Existence, smoothness, approximation, and attractiveness of a locally integral manifold are established for a two time-scales discrete-time system. This manifold contains all the solutions remaining in a specific compact subset. It allows us to define locally a triangular system which is topologically orbitally equivalent with asymptotic phase. It follows that (in)stability properties and existence of solutions of the original system, remaining after some time instant in the above-mentioned compact subset, can be established from the study of a reduced-order system. We study this reduced-order system for a weakly nonstationary case, applying the stroboscopic method to approximate it by a practically meaningful, slowly time-varying system.     

Construction of bode envelopes using REP based range finding algorithms

The frequency domain analysis of systems is an important topic in control theory. Powerful graphical tools exist in classic control, such as the Nyquist plot, Bode plots, and Nichols chart. These methods have been widely used to evaluate the frequency domain behavior of system. A literature survey shows that various approaches are available for the computation of the frequency response of control systems under different types of parametric dependencies, such as affine, multi-linear, polynomial, etc. However, there is a lack of tools in the literature to construct the Bode envelopes for the general nonlinear type of parametric dependencies. In this paper, we address the problem of computation of the envelope of Bode frequency response of a non-rational transfer function with nonlinear parametric uncertainties varying over a box. We propose two techniques to compute the Bode envelopes:first, based on the natural interval extensions (NIE) combined with uniform subdivision and second, based on the existing Taylor model combined with subdivision strategy. We also propose the algorithms to further speed up both methods through extrapolation techniques.     

A revision of root locus method with applications

The paper investigates applications of the root-locus (RL) method to analysis and design of closed loop systems with arbitrary loop transfer functions. Novel analytic sketching rules have been derived first. These rules are applicable to a wide range of transfer functions: rational, fractional and non-rational ones in general, those with time-delays incorporated at various locations, as well as transfer functions describing distributed-parameter systems. An original, straightforward numerical procedure for plotting the root locus has been proposed next. By means of the derived techniques, a generalization of the pole-placement method, which is applicable to control design of both rational and non-rational processes has been proposed also. Finally, it has been shown that RL technique can be very effectively used to investigate the influence of open loop dead-time variations to closed loop poles. It is of particular interest to stress that the techniques proposed and analyzed in this work are exact, in the sense that no rational approximations of infinite-dimensional systems have been utilized. All results have been thoroughly illustrated by numerical examples.     

Input-to-State Stability of Time-Delay Systems: A Link With Exponential Stability

The main contribution of this technical note is to establish a link between the exponential stability of an unforced system and the input-to-state stability (ISS) via the Liapunov–Krasovskii methodology. It is proved that a system which is (globally, locally) exponentially stable in the unforced case is (globally, locally) input-to-state stable when it is forced by a measurable and locally essentially bounded input, provided that the functional describing the dynamics in the unforced case is (globally, on bounded sets) Lipschitz and the functional describing the dynamics in the forced case satisfies a Lipschitz-like hypothesis with respect to the input. Moreover, a new feedback control law is provided for delay-free linearizable and stabilizable time-delay systems, whose dynamics is described by locally Lipschitz functionals, by which the closed-loop system is ISS with respect to disturbances adding to the control law, a typical problem due to actuator errors.      

Adding an integrator for the stabilization problem

We study the relationship between the following two properties: P1: The system is locally asymptotically stabilizable; and P2: The system is locally asymptotically stabilizable; where . Dayawansa, Martin and Knowles have proved that these properties are equivalent if the dimension n = 1. Here, using the so called Control Lyapunov function approach, (a) we propose another more constructive and somewhat simpler proof of Dayawansa, Martin and Knowles's result; (b) we show that, in general, P1 does not imply P2 for dimensions n larger than 1; (c) we prove that P2 implies P1 if some extra assumptions are added like homogeneity of the system. By using the latter result recursively, we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form.