非线性广义最小方差控制律综述

如何设计简单的控制策略对复杂非线性系统进行控制是控制界还未解决的难题．非线性广义最小方差控制律的提出使得非线性控制器的设计可以基于更为一般的非线性模型，并且控制器易于实现．整个系统包含时滞环节，稳定的非线性输入子系统和一个可以用多项式或者状态空间描述的子系统．通过最小化由误差加权项、状态加权项和输入加权项组成的信号的方差得到优化控制器．在系统为开环稳定的情况下，可用史密斯预估器进行控制．本文首先介绍了非线性广义最小方差控制的发展进程，然后综述了基于状态空间和多项式描述的系统的非线性广义最小方差控制器的设计以及其现状和今后的发展方向．     

基于自适应神经网络的一类不确定非线性系统的鲁棒H∞控制

针对一类不确定非线性多输入时变系统，提出了一种新的鲁棒H∞控制方案．通过引入2个自适应神经网络逼近器，提出了一个简化的Hamilton—Jaeobi—like不等式，并据此设计了非线性H∞控制器和匹配不确定项补偿控制器，消除了输入摄动项和估计器最优逼近误差的有界性假设．机器人系统的鲁棒跟踪控制仿真算例证实了所提出控制方案的有效性．     

非线性零阶接近有界多模型神经网络自适应控制器

针对一类单变量非线性离散时间系统,提出一种零阶接近有界的多模型神经网络自适应控制器。该控制器包含一个非线性鲁棒自适应控制器和一个非线性神经网络自适应控制器。当系统非线性项放宽到零阶接近有界时,这两个控制器分别用于保证系统的稳定性和提高系统的性能,系统的控制输入由切换机构在两个控制器之间进行切换产生。最后给出了稳定性和收敛性证明,并通过仿真实验验证了该控制器的有效性。     

一种推广的组合非线性输出反馈控制

针对多变量饱和线性系统的时变参考输入跟踪问题,研究了一种组合非线性输出反馈控制器的设计方法.基于原始的组合非线性反馈理论,构造了全阶和降阶输出反馈控制器.控制器由线性输出反馈项和非线性反馈项组成,使得闭环系统在包含于吸引域的不变集内渐近稳定.除了能够跟踪时变参考输入外,系统还具有良好的动态性能.仿真结果说明了所开发控制器的有效性.     

一类不确定非线性系统反步自适应神经网络控制研究

针对合有高阶不确定扰动项且不可参数线性化的一类非线性系统，采用反步递推方法设计基于多层神经网络的自适应控制器，多层神经网络可较好地逼近非线性系统，其权值能在系统先验知识不多的情况下在线调整，给出了神经网络Lyapunov意义下稳定的在线自适应律，在设计控制器的过程中，采用类加权形式Lyapunov函数，使得控制器能有效处理自适应控制奇异性问题，仿真结果表明，该控制器对系统参数的不确定性和有界干扰具有一定的鲁棒性，并能保证闭环系统全局稳定。     

非线性系统有输入饱和时基于平方和的鲁棒模型预测控制器

本文针对带有参数不确定和输入饱和的单输入单输出(SISO)仿射非线性系统,利用反馈线性化,将非线性系统转化为带有扰动和状态依赖输入饱和的多胞线性参变(LPV)模型,进而提出一种基于平方和(SOS)的鲁棒模型预测控制器(RMPC)设计方法.基于多胞RMPC控制器,设计加权状态反馈控制律,通过引入范数有界定理,确保扰动下预测状态收敛到不变集内,并利用勒让德多项式近似和SOS技术,将状态依赖输入饱和约束转化为多项式凸优化问题,以获得实际和辅助状态反馈律,所设计的SOS-RMPC控制器能够保证闭环系统的稳定性.通过与常规多胞RMPC控制器的仿真比较,验证了本方法的有效性,并进一步仿真分析了勒让德多项式阶次对控制器性能的影响.     

具有输入饱和的电液伺服位置系统自适应动态面控制

针对具有非线性、参数不确定性及输入饱和问题的电液伺服位置系统,提出了一种自适应动态面控制器的设计方法.该方法充分考虑饱和特性,利用双曲正切函数和辅助控制信号对系统非线性模型进行等价变换,进而采用动态面方法设计抗饱和控制器.设计过程中引入Nussbaum函数,以补偿输入饱和引起的非线性项.通过构造合适的Lyapunov函数,证明闭环系统的所有信号一致最终有界.仿真结果表明,所设计的控制器具有良好的跟踪效果,并有效地削弱了输入饱和对系统造成的不良影响.     

带有摄动死区输入的未知非线性系统自适应模糊控制

用自适应模糊控制来实现对带有摄动死区输入的一类未知非线性系统的控制. 文中给出了一种新的死区执行器模型, 该模型含有时变并且摄动的执行增益. 通过将死区非线性分解为一个线性类似项, 一个非线性项和一个扰动类似项降低了扰动类似项的上界, 从而可以用更小的控制力度来实现系统的鲁棒性. 利用反步后推技术与非线性参数化的模糊逼近器结合导出控制器, 该设计取消了模糊基函数须事先已知的限制. 本文不仅从理论上证明了所给控制器能够保证闭环系统的稳定性和预期的跟踪性能, 还用仿真实验验证了控制器的有效性.     

带有死区输入的非线性系统的自适应控制

针对一类具有死区非线性输入的非线性系统,同时考虑系统中存在未建模不确定项,设计了自适应控制器及未知参数的自适应估计率.该控制器使得闭环系统全局稳定且实现了输出信号对参考信号的精确跟踪.仿真结果进一步证实了该控制器能对未知死区及未建模动态进行有效的补偿。     

具有在线选择加权项的隐式自校正控制器*

本文将自校正控制器和零极点配置策略结合起来提出了具有在线选择加权项的两种自校正控制器。采用隐式方式来实现加权项的选择和自校正控制器。本文还证明了这两种控制器具有整体稳定性和收敛性,并给出了仿真实例。     

An online GA-based output-feedback direct adaptive fuzzy-neural controller for uncertain nonlinear systems.

In this paper, we propose a novel design of a GA-based output-feedback direct adaptive fuzzy-neural controller (GODAF controller) for uncertain nonlinear dynamical systems. The weighting factors of the direct adaptive fuzzy-neural controller can successfully be tuned online via a GA approach. Because of the capability of genetic algorithms (GAs) in directed random search for global optimization, one is used to evolutionarily obtain the optimal weighting factors for the fuzzy-neural network. Specifically, we use a reduced-form genetic algorithm (RGA) to adjust the weightings of the fuzzy-neural network. In RGA, a sequential-search -based crossover point (SSCP) method determines a suitable crossover point before a single gene crossover actually takes place so that the speed of searching for an optimal weighting vector of the fuzzy-neural network can be improved. A new fitness function for online tuning the weighting vector of the fuzzy-neural controller is established by the Lyapunov design approach. A supervisory controller is incorporated into the GODAF controller to guarantee the stability of the closed-loop nonlinear system. Examples of nonlinear systems controlled by the GODAF controller are demonstrated to illustrate the effectiveness of the proposed method.     

Implications of dissipativity,inverse optimal control,and stability margins for nonlinear stochastic feedback regulators

In this paper, we derive stability margins for optimal and inverse optimal stochastic feedback regulators. Specifically, gain, sector, and disk margin guarantees are obtained for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton‐Jacobi‐Bellman controllers that minimize a nonlinear‐nonquadratic performance criterion with cross‐weighting terms. Furthermore, using the newly developed notion of stochastic dissipativity, we derive a return difference inequality to provide connections between stochastic dissipativity and optimality of nonlinear controllers for stochastic dynamical systems. In particular, using extended Kalman‐Yakubovich‐Popov conditions characterizing stochastic dissipativity, we show that our optimal feedback control law satisfies a return difference inequality predicated on the infinitesimal generator of a controlled Markov diffusion process if and only if the controller is stochastically dissipative with respect to a specific quadratic supply rate.     

不确定中立型系统鲁棒稳定及镇定的时滞相关准则

This paper concerns problem of the delay-dependent robust stability and stabilization for uncertain neutral systems. Some new delay-dependent stability criteria are derived by taking the relationship between the terms in the Leibniz-Newton formula into account. Free weighting matrices are given to express the relationship between the terms in the Leibniz-Newton formula and the new criteria are based on linear matrix inequalities such that the free weighting matrices can be easily obtained. Moreover, the stability criteria are also used to design the state-feedback controller. Numerical examples demonstrates that the proposed criteria are effective and are an improvement over the previous papers.     

New results on delay‐dependent stability analysis and stabilization for stochastic time‐delay systems

This paper investigates the problems of stability analysis and stabilization for stochastic time‐delay systems. Firstly, this paper uses the martingale theory to investigate expectations of stochastic cross terms containing the Itô integral. On the basis of this, an improved delay‐dependent stability criterion is derived for stochastic delay systems. In the derivation process, the mathematical development avoids bounding stochastic cross terms, and neither model transformation method nor free‐weighting‐matrix method is used. Thus, the method leads to a simple criterion and shows less conservatism. Secondly, on the basis of this stability result, this paper further proposes a state‐feedback controller that exponentially stabilizes the stochastic delay system by a strict LMI. Therefore, unlike previous results, it is not necessary to transform the nonlinear matrix inequalities into LMIs by the cone complementarity linearization method or parameter‐tuning method, which always yield a suboptimal solution. Finally, examples are provided to demonstrate the reduced conservatism of the proposed conditions.Copyright © 2013 John Wiley & Sons, Ltd.     

Fast adaptive fault estimation and accommodation for nonlinear time‐varying delay systems

This paper studies the problem of fault estimation and accommodation for a class of nonlinear time‐varying delay systems using adaptive fault diagnosis observer (AFDO). A novel fast adaptive fault estimation algorithm that does not need the derivative of the output vector is proposed to enhance the performance of fault estimation. Meanwhile, a delay‐dependent criteria is obtained based on free weighting matrix method with the purpose of reducing the conservatism of the AFDO design. On the basis of fault estimation, an observer‐based fault‐tolerant controller is designed to guarantee the stability of the closed‐loop system. In terms of matrix inequality, we derive sufficient conditions for the existence of the adaptive observer and fault‐tolerant controller. Simulation results are presented to illustrate the efficiency of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一类非线性离散时间系统的自适应控制

针对一类非线性离散系统, 利用Lyapunov方法和加权最小二乘估计设计了一种自适应控制器, 在不对非线性加增长条件约束的情况下, 得到了闭环系统的全局跟踪性能.     

Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems

A new hybrid direct/indirect adaptive fuzzy neural network (FNN) controller with a state observer and supervisory controller for a class of uncertain nonlinear dynamic systems is developed in this paper. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an observer-based output feedback control law and adaptive law, is a combination of direct and indirect adaptive FNN controllers. A weighting factor, which can be adjusted by the tradeoff between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive FNN controller and direct adaptive FNN controller. Furthermore, a supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be deactivated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Two nonlinear systems, namely, inverted pendulum system and Chua's (1989) chaotic circuit, are fully illustrated to track sinusoidal signals. The resulting hybrid direct/indirect FNN control systems show better performances, i.e., tracking error and control effort can be made smaller and it is more flexible during the design process.     

Output-feedback sampled-data polynomial controller for nonlinear systems

This paper presents the stability analysis and control synthesis for a sampled-data control system which consists of a nonlinear plant and an output-feedback sampled-data polynomial controller connected in a closed loop. The output-feedback sampled-data polynomial controller, which can be implemented by a microcontroller or a digital computer, is proposed to stabilize the nonlinear plant. Based on the Lyapunov stability theory, stability conditions in terms of sum of squares are obtained to guarantee the stability and to aid the design of a polynomial controller. A simulation example is given to demonstrate the effectiveness of the proposed control approach.