非线性网络控制系统的保性能控制

针对网络诱导时延小于一个采样周期的非线性网络控制系统,研究了系统的稳定性和保性能控制问题.对于T-S模糊模型描述的非线性被控对象,将时延的不确定性转化为系统参数的不确定性,从而将这一类非线性网络控制系统建模为具有参数不确定性的离散T-S模糊模型.基于建立的模型,提出了存在稳定保性能控制器的充分条件,并得出了相应的线性矩阵不等式(LMI)形式.最后通过对永磁同步电动机混沌系统进行控制和仿真研究,验证了所提出方法的有效性.     

一类具有饱和因子的奇异时滞系统的鲁棒保性能控制

研究了具有饱和因子的非线性奇异时滞系统的鲁棒保性能控制问题.目的是设计一个鲁棒控制器和保成本控制器,通过线性矩阵不等式方法(LMI)得出了鲁棒控制器和保性能控制器存在的充分条件.当这些LMI方法是可解时,分别给出了鲁棒控制器和保性能控制器的解析表达式.     

Guaranteed Output Feedback Control for Uncertain Systems under Control and State Constraints

This paper deals with output feedback control of uncertain nonlinear dynamic systems in the presence of state and control constraints. We provide necessary and sufficient conditions for the guaranteed viability property defined by the existence of a Lipschitz closed-loop that maintains exactly the state of the system in a given closed domain of constraints despite some bounded disturbances acting both on the dynamics and on the output. Using the notion of Lipschitz kernel of a closed set-valued map, we obtain some equivalent geometric and Hamilton–Jacobi–Isaac conditions for the guaranteed viability property. We derive an algorithm to build a guaranteed viable output feedback.     

Maximum Principle for Nonlinear Cooperative Elliptic Systems on R^N

We investigate in this work necessary and sufficient conditions for having a Maximum Principle for a cooperative elliptic system on the whole R^N. Moreover, we prove the existence of solutions by an approximation method for the considered system.     

Robust Guaranteed Cost Decentralized Stabilization for Uncertain Discrete Large-Scale Systems with Delays via State Feedback and Output Feedback

The problem of robust guaranteed cost decentralized stabilization for uncertain discrete large-scale systems with delays is investigated in this paper. Sufficient conditions for the existence of the robust guaranteed cost decentralized controllers via memoryless state feedback and static output feedback are expressed as BMIs. Furthermore, alternate iterative algorithms are proposed to solve the feasible problems with BMI constrains. Numerical examples are given to illustrate effectiveness of the proposed methods.     

模糊不确定时滞系统的保成本控制

讨论了基于T-S模型的不确定时滞系统的保成本控制问题.文章采用并行补偿状态反馈控制方法和时滞相关稳定性分析方法,通过引入一个带调节因子的Lyapunov-Krasovskii泛函,利用线性矩阵不等式的形式给出了状态反馈控制器存在的充分条件.当调节因子取不同值时,最小保成本值和反馈增益也是不同的,不同的反馈增益导致不同的动态性能,因此,可以通过选取合适的调节因子来优化闭环系统的动态性能. 最小保成本值可以看作调节因子的函数,因此,可以通过求解一个凸优化问题来求得最小的保成本值和最优的调节因子,文章给出了一个求解最小保成本值的算法.并利用仿真示例验证了所给方法的有效性.     

不确定线性系统的最优保性能可靠控制

针对一类不确定线性系统,采用连续增益故障模型提出了考虑执行器故障的保性能可靠控制问题.通过对具有执行器增益故障的系统分析,利用线性矩阵不等式(LMI)分别给出了保性能标准控制、最优保性能标准控制、保性能可靠控制、最优保性能可靠控制存在的充分条件.根据凸优化理论,最优保性能标准控制和最优保性能可靠控制的设计方法转化为一个线性凸优化算法.仿真数例验证了文中所提出方法的可行性.在相同形式的故障发生时,比较最优保性能标准控制与最优保性能可靠控制,进一步说明了最优保性能可靠控制的必要性.     

Optimal Guaranteed Cost Control of Linear Systems with Mixed Interval Time-Varying Delayed State and Control

This paper deals with the problem of optimal guaranteed cost control for linear systems with interval time-varying delayed state and control. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. A linear–quadratic cost function is considered as a performance measure for the closed-loop system. By constructing a set of augmented Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a guaranteed cost controller design is presented and sufficient conditions for the existence of a guaranteed cost state-feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.     

Novel Optimal Guaranteed Cost Control of Uncertain Discrete Systems with Both State and Input Delays

The problem of the guaranteed cost control (GCC) for a class of uncertain discrete-time systems with both state and input delays is considered in this paper. A novel LMI-based approach is proposed for the existence of a state feedback controller which guarantees not only the asymptotic stability of the closed-loop system, but also an adequate performance bound over all the possible parameter uncertainties. A convex optimization algorithm is given to design the state feedback controller which minimizes a bound on a quadratic performance index. The result exhibits some favorable features in computation as shown by a numerical example. This work was supported by the National Science Foundation of China under Grants 60504012 and 60774039.     

Delay-Dependent Criterion for Guaranteed Cost Control of Neutral Delay Systems

In this article, the guaranteed cost control problem for a class of neutral delay systems is investigated. A linear--quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov method, delay-dependent criteria, which are expressed in terms of matrix inequalities, are proposed to guarantee the asymptotic stability of the system. The matrix inequalities can be solved easily by various efficient optimization algorithms.     

不确定离散时滞模糊系统的保性能控制

针对一类模糊模型表示的，具有范数有界时变参数不确定性离散时滞系统，研究了保性能控制器设计问题。首先推导了保性能控制器存在的充分条件，在此基础上通过求解等价的线性矩阵不等式给出了控制器的设计方法和参数表示。     

Semidefinite Programming Techniques for Reduced Order Systems with Guaranteed Stability Margins

In this paper, the compensator based reduced order control design framework of Burns and King (J. Vibrations and Control, vol. 4, pp. 297–323, 1998) is modified to yield low order systems with guaranteed stability margins. This result is achieved through use of a logarithmic barrier function. In addition, a reduced basis method is formulated in which the compensator equations are approximated on uneven grids; guaranteed stability margins are also included. The methods are tested numerically on a one dimensional, nonlinear, damped, hyperbolic structural control problem. Examples are provided to illustrate differences between systems designed by both reduced basis methods.     

Robust Stabilization by Dynamic Combined State and Output Feedback Compensator for Nonlinear Systems with Jumps

This paper deals with the robustness of the class of nonlinear systems with Markovian jumping parameters and unknown but bounded uncertainties. Under the assumption that the Markovian jump process (disturbance) is irreducible and under complete access to the system state and its mode, we establish robust stability results in two cases: (i) under matching conditions; and (ii) under bounded uncertainties.Research of this author was supported by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0036444     

Fuzzy Partial State Feedback Control of Discrete Nonlinear Systems with Unknown Time-Delay

A new discrete-time fuzzy partial state feedback control method for the nonlinear systems with unknown time-delay is proposed. Ma et al. proposed the design method of the fuzzy controller based on the fuzzy observer and Cao and Frank extend this result to be applicable to the case of the nonlinear systems with the time-delay. However, the time-delay is likely to be unknown in practical. In this paper, the sufficient condition for the asymptotic stability is derived with the assumption that the time-delay is unknown by applying Lyapunov–Krasovskii theorem and this condition is converted into the LMI problem.     

一致稳定合作系统的全局稳定性

本文讨论了一类合作系统的解的收敛性.其基本假设是Jacobi矩阵在中一致稳定．在这个假设下,我们对这类系统给出了完整的全局性态．本文的主要结果如下：如果系统有一个正平衡点,那么它在Int中全局渐近稳定,并给出了系统的非负平衡点全局渐近稳定的充分必要条件．     

非线性半参数回归模型的最大经验似然估计

对于非线性半参数回归模型的估计问题,利用经验似然方法,给出了回归系数,光滑函数以及误差方差的最大经验似然估计.在一定条件下证明了所得估计量的渐近正态性和相合性.     

Feedback Control Methodologies for Nonlinear Systems

A number of computational methods have been proposed in the literature to design and synthesize feedback controls when the plant is modeled by nonlinear dynamics. However, it is not immediately clear which is the best method for a given problem; this may depend on the nature of the nonlinearities, size of the system, whether the amount of control used or time needed for the method is a concern, and other factors. In this paper, a comprehensive comparison study of five methods for the synthesis of nonlinear control systems is carried out. The performance of the methods on several test problems are studied, and some recommendations are made as to which feedback control method is best to use under various conditions.     

Regularity for Certain Nonlinear Parabolic Systems

Abstract

By means of an inequality of Poincaré type, a weak Harnack inequality for the gradient of a solution and an integral inequality of Campanato type, it is shown that a solution to certain degenerate parabolic system is locally Hölder continuous. The system is a generalization of p-Laplacian system. Using a difference quotient method and Moser type iteration it is then proved that the gradient of a solution is locally bounded. Finally using the iteration and scaling it is shown that the gradient of the solution satisfies a Campanato type integral inequality and is locally Hölder continuous.