一类高阶次随机非线性系统的状态反馈镇定

针对一类高阶次随机非线性系统,研究其状态反馈镇定问题.基于最近发展起来的增加幂次积分器技术,通过适当地选取Lyapunov函数和设计参数,给出了一个光滑的状态反馈反推控制器的设计过程,所设计的控制器保证了闭环系统在原点处的平衡点是概率意义下全局渐近稳定的.     

严格反馈随机非线性系统风险灵敏度输出反馈控制器设计

研究了一类严格反馈随机非线性系统的输出反馈设计问题.在无限时区风险灵敏度指标下,应用积分反推(integrator backstepping)技术,设计了控制器.所设计的控制器能够保障对任意风险灵敏度系数具有任意小的指标,并且闭环系统为概率意义下有界的.特别地,所设计的控制器还能保证控制器的平衡条件.仿真例子验证了理论结果的正确性.     

一类上三角随机非线性系统的输出反馈控制

针对一类上三角随机非线性系统的输出反馈控制问题,首先利用反推技术,为其对应的标称系统设计稳定的输出反馈控制器;然后利用低增益齐次占优技术,为整个系统设计输出反馈控制器.所设计的控制器能保证闭环系统的平衡点为依概率全局渐近稳定的,并将低增益齐次占优技术推广到了随机系统,首次解决了一类上三角随机系统的镇定问题.最后通过数值仿真验证了所提出控制方案的有效性.     

系统的增速依赖于不可测状态非线性系统全局输出反馈渐近镇定

研究了一类非线性增长速度依赖于不可测状态且有稳定零动态非线性系统的全局输出反馈渐近稳定控制问题. 因所研究的系统隐含有零动态, 所以首先定义了一系列新的线性变换, 从而成功地分离出原系统的零动态, 得到了便于输出反馈设计的新系统. 然后给出了变换后系统的较为简洁的输出反馈控制设计过程, 并且, 闭环系统的渐近稳定性可由所导出矩阵的正定性来保证. 最后, 仿真算例验证了文中理论结果的正确性.     

非线性随机时滞系统输出反馈镇定

研究了非线性随机时滞系统的镇定问题，运用Backstepping递推设计方法，得到了使得非线性随机时滞系统镇定的输出反馈控制器的设计算法。     

随机非线性系统鲁棒自适应反馈控制器的积分反推方法设计

考虑了一类随机非线性系统的鲁棒自适应控制问题.采用Ito随机微分方程描述系统,进而在概率意义下研究系统的鲁棒稳定性.应用积分反推(backstepping)方法,系统地给出了设计状态反馈及输出反馈鲁棒自适应控制器的方法.同时构造出了适当形式的四次型的自适应控制Lyapunov函数(CLF).     

非线性系统输出反馈控制

本文针对一般非线性系统,构造了迭代学习观测器,基于该迭代学习观测器的状态和可调参数设计了输出反馈控制律,通过选择可调参数自适应调节律的适当形式,保证了整个系统的渐近稳定性和输出反馈控制律的有界性。计算机模拟显示所提出方法的有效性。     

非线性微分——代数系统的输出反馈镇定控制

对满足线性增长条件的非线性微分--代数系统, 研究了其输出反馈镇定控制问题. 通过将状态观测器与控制器耦合在一起设计, 构造出一种非初始化的线性高增益状态观测器, 具有良好的鲁棒性. 基于反推设计方法构造出一个线性的动态输出补偿器, 使得整个闭环系统是渐近稳定的. 仿真结果验证了本文所提控制方法的有效性.     

一类非齐次高阶非线性系统的连续反馈控制设计

研究了一类非齐次的高阶非线性系统的连续状态反馈控制设计问题. 通过定义一列适当的辅助函数,放宽了对非线性项的约束条件. 利用传统的积分反推技术,并增加一个积分项的方法,得到了这类系统的稳定性,给出了控制器的设计方法,并通过一个例子验证了本文的理论结果.     

非线性随机时滞系统输出反馈镇定

研究了非线性随机时滞系统的镇定问题. 运用Backstepping递推设计方法, 得到了使得非线性随机时滞系统镇定的输出反馈控制器的设计算法.     

Decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems

Under the weaker conditions on the drift and diffusion terms, this paper focuses on the global decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems. By introducing an appropriate coordinate transformation, the original system is transformed into an equivalent one with tunable gain. After that, by reasonably combing the homogeneous domination approach with stochastic nonlinear systems stability criterion, and skillfully choosing the low gain scale, the decentralised output-feedback controller is constructed for each subsystem to ensure that the closed-loop system is globally asymptotically stable in probability. The simulation example is given to demonstrate the effectiveness of the proposed design scheme.     

Output-feedback control of a class of high-order stochastic nonlinear systems

This article investigates the problem of output-feedback stabilisation for a class of high-order stochastic non-linear systems in which the diffusion terms depend on unmeasurable states besides the output. By introducing a new rescaling transformation, adopting an effective observer and choosing the appropriate Lyapunov function, an output-feedback controller is constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, the output can be regulated to the origin almost surely, and the problem of inverse optimal stabilisation in probability is solved. The efficiency of the output-feedback controller is demonstrated by several simulation examples.     

一类高阶次随机非线性系统的输出反馈镇定

针对一类高阶次随机非线性系统,研究其输出反馈镇定问题．通过选择有效的观测器和李雅普诺夫函数,所设计的光滑输出反馈控制器保证了闭环系统的平衡点是依概率全局渐近稳定的,输出几乎处处调节到零．数值仿真验证了控制方案的有效性．     

Approximation-based adaptive fuzzy control for a class of non-strict-feedback stochastic nonlinear systems

This paper considers the problem of adaptive fuzzy control of a class of single-input/single-output （SISO） nonlinear stochastic systems in non-strict-feedback form. Fuzzy logic systems are used to approximate the uncertain nonlinearities and backstepping technique is utilized to construct an adaptive fuzzy controller. The proposed controller guarantees that all the signals in the resulting closed-loop system are bounded in probability. The main contribution of this note lies in providing a control strategy for a class of nonlinear systems in non- strict-feedback form. Simulation result is used to test the effectiveness of the suggested approach.     

Improved stability and instability theorems for stochastic nonlinear systems

This paper focuses on sufficient conditions which make stochastic nonlinear systems stable and unstable. A series of new stability (instability) criteria, which admit the infinitesimal operator of Lyapunov (Lyapunov‐like or Chetaev) functions to be indefinite, are proposed using the uniformly asymptotically stable function. The obtained stability and instability theorems weaken the constraints on Lyapunov and Lyapunov‐like (or Chetaev) functions, respectively. Many existing classical stability and instability criteria can be regarded as special cases of the stability and instability results in this paper. Finally, the presented theoretical results are illustrated by some simulation examples.     

Global stabilization of uncertain stochastic nonlinear time‐delay systems by output feedback

Constructive control techniques have been proposed for controlling strict feedback (lower triangular form) stochastic nonlinear systems with a time‐varying time delay in the state. The uncertain nonlinearities are assumed to be bounded by polynomial functions of the outputs multiplied by unmeasured states or delayed states. The delay‐independent output feedback controller making the closed‐loop system globally asymptotically stable is explicitly constructed by using a linear dynamic high‐gain observer in combination with a linear dynamic high‐gain controller. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input

This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.     

Adaptive neural tracking control for a class of stochastic nonlinear systems

This paper investigates the problem of adaptive neural control design for a class of single‐input single‐output strict‐feedback stochastic nonlinear systems whose output is an known linear function. The radial basis function neural networks are used to approximate the nonlinearities, and adaptive backstepping technique is employed to construct controllers. It is shown that the proposed controller ensures that all signals of the closed‐loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. The salient property of the proposed scheme is that only one adaptive parameter is needed to be tuned online. So, the computational burden is considerably alleviated. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Command filter-based adaptive fixed-time fault-tolerant control for stochastic nonlinear systems with actuator hysteresis

In this paper, an adaptive fault-tolerant fixed-time control problem is considered via command-filter technique for stochastic nonlinear systems with sensor fault and actuator hysteresis. With the application of command-filtering technique, a novel command-filter compensate mechanism is designed, which implies that the improved control scheme not only eliminates “the explosion of complexity” but also realizes the compensate signal is bounded within fixed-time interval. The unavailability of state variables caused by sensor fault is solved by applying parameter separation and regrouping approach. Meanwhile, an adaptive auxiliary signal is designed to cope with the backlash-like hysteresis phenomenon, which can avoid singularity, reduce chattering, and facilitate controller design. Combining backstepping technique and Lyapunov stability theorem, an adaptive fault-tolerant control approach is developed, which can guarantee all closed-loop signals remain semi-globally practical fixed-time stable (SGPFS) in probability. The validity of the proposed strategy is illustrated by simulation examples.