非线性时滞系统自适应模糊动态面控制

针对未知非线性系统控制器设计过程中引入逼近器过多的问题,提出一种简化的自适应模糊动态面控制器设计方案.在控制器设计过程中,仅采用一个模糊逻辑系统作为逼近器,使得所有的未知项得到补偿,同时采用自适应技术在线辨识未知参数和逼近误差上界.文中的控制方案克服了传统backstepping控制器中"复杂性膨胀"的问题.通过构造合适的Lyapunov函数,证明闭环系统的所有信号为半全局最终一致有界.仿真实例验证所提出的控制方案的有效性.     

非线性时滞系统的指数稳定H∞控制

研究非线性时滞系统基于 TS模型的指数稳定 H∞ 控制问题 ,针对一类控制对象 ,得到存在指数稳定 H∞ 模糊控制器的充分条件。此充分条件等价于两类线性矩阵不等式 (LMI)的可解性     

基于观测器的非严格反馈时滞非线性系统的神经网络自适应控制

针对一类非严格反馈的时滞非线性系统, 研究了一类基于观测器的自适应神经网络控制问题.针对系统中存在未知状态变量的问题, 设计了一个状态观测器.利用反步法和径向基神经网络的逼近特性, 提出了一种自适应神经网络输出反馈控制方法.所设计的控制器保证了闭环系统中所有信号的半全局一致有界性.最后, 通过仿真验证了所提控制方法的有效性.     

一类MIMO非线性系统的稳定自适应模糊控制

针对一类 MIMO不确定非线性系统 ,基于一种修改的李亚普诺夫函数并利用 I型模糊系统的逼近能力 ,提出一种分散自适应模糊控制器设计的新方案。该方案不但能够避免现有的一些自适应模糊 /神经网络控制器设计中对控制增益一阶导数上界的要求 ,而且能够避免控制器的奇异问题。通过理论分析 ,证明闭环控制系统是全局稳定的 ,跟踪误差收敛到零。仿真结果表明了该方法的有效性。     

具有类反斜线回滞执行器的非线性系统的自适应控制

针对类反斜线回滞非线性系统,设计了自适应控制器,保持系统稳定并实现对参考信号的任意精度跟踪.在控制器设计中,通过构造足够光滑的非线性函数作为符号函数的逼近,从而解决了传统自适应控制器设计中由于符号函数的引入而导致控制器不连续的问题,避免了因此而产生的抖震现象.在系统模型中充分考虑未建模动态,使模型更具一般性.最后应用MATLAB软件进行仿真实验,结果进一步验证了该控制器的有效性.     

基于圆判据的一种LMI绝对镇定方法

针对非线性Lur'e系统,提出了一种输出反馈控制器综合方法。对于系统在无摄动及线性部分存在乘性范数摄动的情况,分别设计了保证闭环系统绝对稳定的动态输出反馈控制器。由圆判据出发,通过把绝对稳定性问题等价地转化成H∞控制问题,得到了一组由线性矩阵不等式(LMI)表达的控制器存在的充分性条件。     

基于复合干扰观测器的CMG框架系统高精度转速控制

为使控制力矩陀螺(CMG)输出高精度力矩,框架转速必须具有足够高的控制精度.然而,在CMG框架伺服系统中,存在转子动不平衡力矩,齿槽力矩,电流脉动,非线性摩擦等多种干扰,严重影响了框架控制性能.为抑制各种干扰对框架控制性能的影响,文章设计了一种基于复合干扰观测器的非线性鲁棒控制器.首先,将系统中存在的干扰模化为频率已知的周期性干扰和变化率有界的慢变干扰,建立了三阶干扰动态模型,设计了复合干扰观测器,从而实现了对复杂干扰的准确估计.在此基础上,采用backstepping方法设计了框架转速非线性鲁棒控制器,实现系统的反馈控制.针对某CMG框架系统的转速控制仿真表明,该方法是可行的.     

基于复合干扰观测器的CMG框架系统高精度转速控制北大核心CSCD

为使控制力矩陀螺(CMG)输出高精度力矩,框架转速必须具有足够高的控制精度.然而,在CMG框架伺服系统中,存在转子动不平衡力矩,齿槽力矩,电流脉动,非线性摩擦等多种干扰,严重影响了框架控制性能.为抑制各种干扰对框架控制性能的影响,文章设计了一种基于复合干扰观测器的非线性鲁棒控制器.首先,将系统中存在的干扰模化为频率已知的周期性干扰和变化率有界的慢变干扰,建立了三阶干扰动态模型,设计了复合干扰观测器,从而实现了对复杂干扰的准确估计.在此基础上,采用backstepping方法设计了框架转速非线性鲁棒控制器,实现系统的反馈控制.针对某CMG框架系统的转速控制仿真表明,该方法是可行的.     

带积分环节的隶属度函数中心自适应模糊控制器设计

自适应变论域模糊控制是改变模糊控制性能的主要方法之一,针对自适应变论域模糊控制器的稳定性设计这一难题,将输入和输出的隶属度函数分别用论域值表示成解析形式;针对典型模糊控制系统没有考虑积分环节带来的稳态误差问题,设计一种积分器,并从减小控制规则数目的角度出发设计了针对积分环节的控制规则库;引进Lyapunov函数,设计了输入隶属度函数论域值的自适应律和输出隶属度函数中心取值的自适应律,最后针对Duffing非线性系统仿真,结果表明设计的变论域模糊控制器是可行的。     

一类不确定性非线性系统的状态反馈鲁棒自适应控制器的设计与分析

该文考虑一类具有一般不确定性和部分参数未知的非线性系统（1），设计出一种用于跟踪参考信号的状态反馈鲁棒自适应控制器，此控制器对系统参数和状态的不确定性具有鲁棒性，能保证闭环系 统的全局稳定性，并解决了ε 跟踪问题. 仿真结果表明，所设计的鲁棒自适应控制系统具有良好的跟踪性能， 而且控制量在容许控制的范围之内.     

On the Optimal Stabilisation for a set of Programmed Motions of the Bilinear Control System

During recent years there has been considerable interest in using bilinear systems [1, 2] as mathematical models to represent the dynamic behavior of a wide class of engineering, biological and economic systems. Moreover, there are some methods [3] which may approximate nonlinear control systems by bilinear systems. For the first time Zubov has proposed a method of stabilization control synthesis for a set of programmed motions in linear systems [4]. In papers [5, 6] this method has been developed and used to solve the same problem for bilinear systems. In the present paper the following problems are considered. First, synthesis of nonlinear control as feedback under which the bilinear control system has a given set of programmed and asymptotic stable motions. Because this control is not unique, the second problem concerns optimal stabilization. In this paper a method for the design of nonlinear optimal control is suggested. This control is constructed in the form of a convergent series. The theorem on the sufficient conditions to solve this problem is represented.     

Probability-one homotopies in computational science

Probability-one homotopy algorithms are a class of methods for solving nonlinear systems of equations that, under mild assumptions, are globally convergent for a wide range of problems in science and engineering. Convergence theory, robust numerical algorithms, and production quality mathematical software exist for general nonlinear systems of equations, and special cases such as Brouwer fixed point problems, polynomial systems, and nonlinear constrained optimization. Using a sample of challenging scientific problems as motivation, some pertinent homotopy theory and algorithms are presented. The problems considered are analog circuit simulation (for nonlinear systems), reconfigurable space trusses (for polynomial systems), and fuel-optimal orbital rendezvous (for nonlinear constrained optimization). The mathematical software packages HOMPACK90 and POLSYS_PLP are also briefly described.     

An adaptive robust controller for time delay maglev transportation systems

For engineering systems, uncertainties and time delays are two important issues that must be considered in control design. Uncertainties are often encountered in various dynamical systems due to modeling errors, measurement noises, linearization and approximations. Time delays have always been among the most difficult problems encountered in process control. In practical applications of feedback control, time delay arises frequently and can severely degrade closed-loop system performance and in some cases, drives the system to instability. Therefore, stability analysis and controller synthesis for uncertain nonlinear time-delay systems are important both in theory and in practice and many analytical techniques have been developed using delay-dependent Lyapunov function. In the past decade the magnetic and levitation (maglev) transportation system as a new system with high functionality has been the focus of numerous studies. However, maglev transportation systems are highly nonlinear and thus designing controller for those are challenging. The main topic of this paper is to design an adaptive robust controller for maglev transportation systems with time-delay, parametric uncertainties and external disturbances. In this paper, an adaptive robust control (ARC) is designed for this purpose. It should be noted that the adaptive gain is derived from Lyapunov–Krasovskii synthesis method, therefore asymptotic stability is guaranteed.     

Bilinear Control and Application to Flexible a.c. Transmission Systems

The purpose of this paper is an integrated overview of bilinear systems (BLS) research which has evolved over the past few decades, and a new result on control of flexible a.c. transmission systems (FACTS) is presented. BLS may be derived in many cases from principles of physics, chemistry, biology, socioeconomics, and engineering. In other cases, BLS are more accurate approximations to nonlinear systems than are traditional linear systems, as shown for example by the added bilinear terms (in state and control) for the Taylor series.While an appropriately designed linear control system may be optimum relative to some quadratic performance index without added constraints, bilinear or parametric control can be designed to improve more global performance and indeed to increase the region of attainable states. Such controllability and stabilization of BLS and of a series line-capacitor controlled FACTS is presented.     

Sufficient stability conditions and stabilizing control design for delay differential systems of a special type

This paper introduces some sufficient conditions for uniform and asymptotic global stability as well as the algorithms for design of stabilizing control for special systems like cascaded (triangular) systems and integrator chains. The results are presented in terms of semidefinite Lyapunov functions, and they hold for nonlinear nonautonomous systems. Application of the results proposed is illustrated by some classical examples.     

On asymptotic optimization of a class of nonlinear stochastic hybrid systems

We consider the problem of control for continuous time stochastic hybrid systems in finite time horizon. The systems considered are nonlinear: the state evolution is a nonlinear function of both the control and the state. The control parameters change at discrete times according to an underlying controlled Markov chain which has finite state and action spaces. The objective is to design a controller which would minimize an expected nonlinear cost of the state trajectory. We show using an averaging procedure, that the above minimization problem can be approximated by the solution of some deterministic optimal control problem. This paper generalizes our previous results obtained for systems whose state evolution is linear in the control.This work is supported by the Australian Research Council. All correspondence should be directed to the first author.     

Chaotic synchronization of two complex nonlinear oscillators

Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing’s oscillators. Physica A 2001;292:193–206], a system of periodically forced complex Duffing’s oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schrödinger equation has also been pointed out.In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.     

非线性退化时滞微分控制系统的函数能控性

本文讨论非线性退化时滞微分控制系统．首先就非线性退化时滞微分控制系统的一阶变分系统给出变易公式,然后就非线性退化时滞微分控制系统的一阶变分系统的函数能控性给出一些判据,最后给出关于非线性退化时滞微分控制系统的函数能控性的判据．     

Synchronization of nonlinear systems with delays via periodically nonlinear intermittent control

In this paper, the synchronization for a class of nonlinear chaotic systems with delays is proposed by using periodically intermittent nonlinear feedback control. Some synchronization criteria are derived based on Lyapunov functional theory and several differential inequalities such as Halanay inequality. As a special case, some sufficient conditions are obtained to ensure the synchronization of nonlinear systems without delays. Finally, some numerical simulations are presented to verify the theoretical results.