基于非线性观测器设计的混沌同步控制

提出一种基于非线性观测器设计的混沌同步控制方法,给出了一类含有不确定参数混沌系统的观测器实现条件.该控制策略可满足混沌系统中存在一些不确定参数的要求.通过对Lorenz混沌系统的理论分析和数字仿真,证明了其有效性.     

Robust analysis and control for a class of uncertain nonlinear discrete-time systems

This paper deals with the problem of robust analysis and control of a class of nonlinear discrete-time systems with (constant) uncertain parameters. For the analysis problem we use a polynomial Lyapunov function and we generalize, for nonlinear systems, the “extended stability” notion proposed by Oliveira et al. (1999) in the context of linear discrete-time uncertain systems. As a result, we propose an LMI optimization problem to maximize an estimate of the domain of attraction, and also extend this approach to the synthesis problem by considering parameter-dependent Lyapunov functions and nonlinear multipliers. Numerical examples illustrate the approach and show its potential for solving analysis and control problems of nonlinear discrete-time systems.     

Necessary and sufficient conditions for quadratic controllability of a class of uncertain systems

We introduce a controllability notion for uncertain systems, namely, quadratic controllability. For a specific class of norm bounded uncertain systems, we show that this notion is equivalent to controllability of a nominal system and the satisfaction of a certain structural condition by the uncertainty. For systems in which the uncertain parameters affect all control inputs, this structural condition is simply the familiar matching condition commonly encountered in the literature on robust and adaptive control of uncertain systems.     

一类具有Markov跳跃参数的不确定混合线性时滞系统鲁棒稳定性研究

讨论了一类具有Markov跳跃参数的不确定混合线性时滞系统的鲁棒稳定性问题．分别给出了非匹配条件下不确定部分范数上界已知时使混合线性系统以概率1渐近稳定的充分条件,和匹配条件下不确定部分范数上界未知时同样可以实现混合系统以概率1渐近稳定的鲁棒自适应控制设计方案．文章研究结果表明,此控制方案对混合线性时滞系统的不确定部分是有效的．     

Robust reliability method for non-fragile guaranteed cost control of parametric uncertain systems

The problem of non-fragile guaranteed cost control of uncertain systems is studied from a new point of view of reliability against uncertainties. An efficient robust reliability method for the analysis and design of non-fragile guaranteed cost controller of parametric uncertain systems is presented systematically. By the method, a robust reliability measure of an uncertain control system satisfying required robust performance can be obtained, and the robustness bounds of uncertain parameters such that the control cost of a system is guaranteed can be provided. The optimal non-fragile guaranteed cost controller obtained in the paper may possess optimal guaranteed cost performance satisfying the precondition that the system is robustly reliable with respect to uncertainties occurring in both the controlled plant and controller gain. The presented formulations are in the framework of linear matrix inequality and thus can be carried out conveniently. The presented method provides an essential basis for the tradeoff between reliability and control cost in controller design of uncertain systems. Two numerical examples are provided to demonstrate the efficiency and feasibility of the presented method. It is shown that the coordination and simultaneous realization of the system performance, control cost, and robust reliability in control design of uncertain systems are significant.     

不确定性参数灵敏度分析的随机响应面法

动力学和控制系统中往往包含有不确定性参数,为此提出了一种基于随机响应面的不确定性参数灵敏度分析方法,以量化参数不确定性对响应变异性的影响.文中首先利用随机响应面建立不确定性参数和响应之间的表达式,然后通过求偏导方式推导参数的灵敏度系数,该系数综合反映了参数均值和标准差的影响.最后通过一根包含几何、材料不确定参数的数值梁来验证所提出方法,并与方差分析法结果进行了比较.     

On an output‐feedback stabilization problem with uncertainty in the relative degree

This paper deals with an output‐feedback finite‐time control problem for a class of nonlinear uncertain systems whose relative degree is affected by an uncertain system parameter and is therefore unknown at the stage of control design. We show that an existing second‐order sliding mode control algorithm can address successfully the control task of a finite‐time output‐feedback stabilization when the uncertain relative degree is equal to 1 or 2. We derive constructive tuning rules for the control parameters and show its effectiveness by using computer simulations. Copyright © 2007 John Wiley & Sons, Ltd.     

独立摄动参数不确定线性系统的正实控制

考虑了一类范数有界参数不确定线性系统的鲁棒正实性分析和设计问题,其中参数不确定性是独立摄动的．通过构造增广系统将不确定系统的鲁棒正实分析和控制问题转化为确定系统的情形,给出了鲁棒正实分析问题的线性矩阵不等式解法,导出了输出反馈控制器的存在条件．所得结论将范数有界参数不确定系统的鲁棒正实分析和控制的现有结果推进了一步．     

Adaptive tracking of nonlinear systems with non-symmetric dead-zone input

Quite successfully adaptive control strategies have been applied to uncertain dynamical systems subject to dead-zone nonlinearities. However, adaptive tracking of systems with non-symmetric dead-zone characteristics has not been fully discussed with minimal knowledge of the dead-zone parameters. It is shown that the controlled system preceded by a non-symmetric dead-zone input can be represented as an uncertain nonlinear system subject to a linear input with time-varying input coefficient. To cope with this problem, a new adaptive compensation algorithm is employed without constructing the dead-zone inverse. The proposed adaptive scheme requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. The new control scheme ensures bounded-error trajectory tracking and assures the boundedness of all the signals in the adaptive closed loop. By appropriate selections of the controller parameters, we show that the smoothness of the controller does not affect the accuracy of trajectory tracking control. A numerical example is included to show the effectiveness of the theoretical results.     

An algorithm for the quadratic stabilization of uncertain systems with structured uncertainty of the one-block type 1

The main result of this paper is a sufficient condition for the quadratic stabilizability of a class of uncertain systems containing structured uncertainty. The uncertain systems under consideration are referred to as uncertain systems of the one-block type. The main requirement for such uncertain systems is that the number of (unmatched) uncertain parameters is less than or equal to the number of control inputs. In the quadratic stabilization algorithm presented, the uncertainty structure is exploited by the introduction of scaling parameters. A key advantage of the algorithm presented in this paper is that it is based on the solution of a Lyapunov equation. Moreover, the solution to this Lyapunov equation is a linear function of the scaling parameters. This enables the quadratic stabilizability of the system to be tested by solving a Linear Matrix Inequality problem in which the number of unknown variables is equal to the number of uncertain parameters.     

基于自适应律修改的MIMO非线性系统模糊控制

针对一类不确定多输入多输出(MIMO)非线性系统,提出了一种新的间接自适应模糊控制设计方案,解决了提高模糊控制精度问题。该方法对模糊逻辑系统中的未知参数设计了一种新的自适应学习律,证明了在此自适应律作用下,不但能使跟踪误差收敛到原点的小邻域内,而且通过适当增大设计参数值,可使跟踪误差减小,提高了控制精度。通过对连续发酵过程控制的仿真研究验证了该方法的有效性。     

基于神经网络的不确定随机非线性时滞系统自适应有界镇定

针对一类不确定严格反馈随机非线性时滞系统的自适应有界镇定问题,利用神经网络参数化和Backstepping方法,提出一种新的且含较少学习参数的神经网络自适应控制策略,以保证系统半全局随机有界.稳定性分析证明闭环系统的所有误差信号概率意义下有界.仿真结果表明所提出控制器设计方法的有效性.     

时变不确定多时滞连续系统的最优保成本控制

针对一类同时具有状态多时滞和输入多时滞的时变不确定连续多时滞系统。研究保成本状态反馈控制器的设计。假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件,通过构造改造的Lyapunov函数和线性矩阵不等式（LMI）方法,给出系统满足保性能指标的一个充分条件,仅通过求解一个相应的线性矩阵不等式,就可得到保性能控制器使得闭环系统的一个保成本函数对所有允许的不确定参数有上界。通过求解凸优化问题得到最优保性能控制器,最后用数值例子说明该方法的有效性。     

Robust H2 estimation and control

This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with normbounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities ( LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared tothe existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.     

Robust H_2 estimation and control

This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities (LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared to the existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.     

Robust consensus for networked mechanical systems with coupling time delay

This paper studies the state consensus for a class of networked nonlinear mechanical systems with coupling time delay. In particular, robust consensus protocols for both deterministic and uncertain systems with time delay are investigated. For deterministic systems, we develop a P-like protocol which allows for variable coupling time delay. We show that it is sufficient to have only the relative position information together with a damping control term, whereas the relative velocity information is not needed for state consensus. Then, an adaptive robust control protocol is proposed for uncertain systems with unknown parameters in the system dynamics and arbitrary constant coupling time delays. By introducing the passivity-based framework, we demonstrate that state consensus is still reachable in this case. Finally, a numerical example is included to illustrate the obtained results.     

Robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with parametric uncertainty

The robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with uncertain parameters is studied. Based on the independence of uncertain parameters and stochastic excitations, the non-linear stochastic optimal control for the nominal quasi-Hamiltonian system with average-value parameters is first obtained by using the stochastic averaging method and stochastic dynamical programming principle. Then, the means and standard deviations of root-mean-square responses, control effectiveness and control efficiency for the uncertain quasi-Hamiltonian system are calculated by using the stochastic averaging method and the probabilistic analysis. By introducing the sensitivity of the variation coefficients of controlled root-mean-square responses, control effectiveness and control efficiency to those of uncertain parameters, the robustness of the non-linear stochastic optimal control is evaluated. Two examples are given to illustrate the proposed control procedure and its robustness.     

Improved adaptive fuzzy backstepping control of a magnetic levitation system based on Symbiotic Organism Search

Magnetic levitation systems have become very important in many applications. Due to their instability and high nonlinearity, such systems pose a challenge to many researchers attempting to design high-performance and robust tracking control. This paper proposes an improved adaptive fuzzy backstepping control for systems with uncertain input nonlinear function (uncertain parameters and structure), and applies it to a magnetic levitation system, which is a typical representative of such systems. An adaptive fuzzy system is used to approximate unknown, partially known or uncertain input nonlinear functions of a magnetic levitation system. An adaptation law is obtained based on Ljapunov analysis in order to guarantee closed-loop stability and good tracking performance. Initial adaptive and control parameters have been initialized with Symbiotic Organism Search optimization algorithm, due to strong non-linearity and instability of the magnetic levitation system. The theoretical background of the proposed control method is verified with a simulation study and implementation on a laboratory experimental application.     

一类不确定系统的自适应非奇异Terminal滑模控制

提出针对一类不确定系统的自适应非奇异Terminal滑模控制。确定含非线性项的滑模面,通过构造李亚普洛夫函数的方式确定控制器结构,设计自适应增益控制律实时估计不确定参数,并考虑外扰动的影响,证明控制系统的稳定性和鲁棒性。仿真结果验证自适应非奇异Terminal滑模控制器能够使不确定系统状态变量快速收敛。