On Robust Approximate Feedback Linearization: Control with Two Gain-scaling Factors

In this paper, we consider a problem of global stabilization for a class of approximately feedback linearized nonlinear systems. In order to handle more nonlinearity over the existing results, we provide a new feedback controller with two gain-scaling factors and we show that more nonlinearity can be treated by our control scheme. Moreover, we analytically show that the considered nonlinear systems can be stabilized by the proposed controller. Through comparison practical examples, we illustrate the improved features of our proposed control method.

     

On asymptotic stabilisation of a chain of integrators with nonlinearity and an uncertain input delay by output feedback

In this paper, we provide an output feedback solution over one given by Choi and Lim [Systems & Control Letters, 59(6), 374–379 (2010)] under more generalised system set-up. More specifically, we consider a stabilisation problem of a chain of integrators that has nonlinearity and an uncertain delay in the input by output feedback. The nonlinearity is classified into four types. Then, we propose a memoryless output feedback controller which contains a gain-scaling factor to adjust controller gains depending on the given nonlinearity type. Our stability analysis shows that the controlled system has unique stabilisation result associated with each type of nonlinearity. Our result provides a new aspect to the stabilisation problem of nonlinear time-delay systems and broadens the existing control results of time-delay systems. Two examples are given for illustration.     

A novel on-line OCID method and its application to input-constrained active fault-tolerant tracker design for unknown nonlinear systems

ABSTRACT

The existing off-line observer/controller identification (OCID) method for linear systems is newly extended in this paper for off-line/on-line identification of known/unknown highly nonlinear systems, and a new input-constrained active fault-tolerant tracker is developed, based on the identified linear models. The advantages of the proposed extended on-line OCID method for linear/nonlinear systems are briefly described as follows: (i) Implement novel servo-control-oriented off-line OCID methods in observer and controller canonical forms for highly nonlinear systems; (ii) Is able to overcome the discontinuity induced by the singular value decomposition (SVD) that should be carried out at each sampling instant; (iii) It directly realises the identified parameters in the observer/controller canonical forms; this simplifies the identification process; (iv) Can be practically implemented for the on-line control of an unknown nonlinear system which was constituted by an unknown open-loop plant, an existing but unknown controller and/or an unknown observer; and (v) Can be utilised to develop a new active fault-tolerant controller to compensate the immovable existing controller of the practical operating system. Finally, the servo-control-oriented off-line OCID method for the highly nonlinear PUMA 560 manipulator is shown in the illustrative examples to demonstrate the superiority of the proposed method.     

切换非线性系统的分布式模型预测控制

针对一类具有预先指定切换序列的切换非线性系统,研究了具有通信信道干扰和时滞测量的分布式模型预测控制问题.在每个子系统都存在镇定控制器的假设下,利用基于Lyapunov函数的模型预测控制器设计了分布式模型预测控制器,并给出了闭环切换非线性系统最终有界的充分条件.最后,通过仿真结果表明了分布式模型预测控制策略的有效性.     

Global stabilisation for a class of upper-triangular nonlinear systems with unmodelled dynamics and time-delay

This paper considers the stabilisation control problem of upper-triangular nonlinear time-delay systems. One distinct characteristic of this work is that the systems contain unmodelled dynamics, unknown control coefficients and time-varying delay, which make the control design much more difficult. By modifying the homogeneous domination approach and introducing a gain-scaling method, a new controller is constructed such that all the states of the closed-loop systems are bounded and convergent to the origin. Simulation examples are given to illustrate the validity of the theory.     

Observer-based Finite-time Control of Stochastic Non-strict-feedback Nonlinear Systems

This paper investigates the observer-based adaptive finite-time neural control issue of stochastic non-strict-feedback nonlinear systems. By establishing a state observer and utilizing the approximation property of the neural network, an adaptive neural network output-feedback controller is constructed. The controller solves the issue that the states of stochastic nonlinear system cannot be measured, and assures that all signals in the closed-loop system are bounded. Different from the existing adaptive control researches of stochastic nonlinear systems with unmeasured states, the proposed control scheme can guarantee the finite-time stability of the stochastic nonlinear systems. Furthermore, the effectiveness of the proposed control approach is verified by the simulation results.

     

一类高阶非线性不确定系统自适应稳定控制

研究了一类高阶非线性不确定性系统的自适应稳定控制设计问题.因该系统的非线性程度高,其控制系数不等同、符号已知、但数值未知,故在此之前其稳定控制设计问题没有得到解决.本文应用自适应技术,结合设计参数的适当选取,从而得到了设计该类非线性系统状态反馈稳定控制器的新方法,并基于反推技术,给出了稳定控制器的设计步骤.所设计的状态反馈控制器使得闭环系统的状态全局渐近收敛于零,其余闭环信号一致有界.最后通过一个仿真例子说明了控制设计方法的有效性.     

基于控制系统直接方法的非线性系统预见控制器设计

针对一类非线性离散时间系统给出最优预见控制器设计方法. 首先运用非线性控制系统直接控制方法的思想, 将非线性反馈部分作为形式输入, 使得系统成为“形式上”的线性系统; 然后, 针对该线性系统, 利用最优预见控制的基本方法设计最优预见控制器; 最后, 利用形式输入与实际输入的关系得到非线性离散时间系统的最优预见控制器. 证明了如果形式线性系统满足一定的可镇定和可检测条件, 则闭环系统是渐近稳定的. 数值仿真结果表明了控制器的有效性.

     

基于参数辨识和T-S模糊模型的一类非线性系统镇定控制器设计

针对一类非线性不确定控制系统,首先采用参数辨识的方法构造出对应的Takagi-Sugeno（T-S）模糊模型;然后运用平行分布补偿（PDC）控制器设计方法进行系统的稳定控制器设计;最终达到镇定原非线性系统的目的.给出一种从T-S模糊模型参数辨识到PDC控制器设计的非线性控制器的设计方法.针对单级倒立摆系统的仿真结果验证了所提出方法的有效性.     

Robust approximate feedback linearisation control for nonlinear systems with uncertain parameters and external disturbance: its application to an electromagnetic levitation system

A robust control scheme with a gain-scaling factor is proposed for an extended class of nonlinear systems. Compared with many previous studies, our considered systems are more generalised by including uncertain parameters, perturbed nonlinearities, and external disturbance. With our control scheme, all states of the controlled system remain bounded. Moreover, it is shown that the ultimate bounds of some system states can be made (arbitrarily) small by adjusting the gain-scaling factor depending on the nonlinearities and external disturbance. The effectiveness of our control scheme is experimentally shown via its application in the control of an electromagnetic levitation system.     

Global output-feedback stabilization for a class of stochastic non-minimum-phase nonlinear systems

In this paper, the problem of output-feedback stabilization is investigated for the first time for a class of stochastic nonlinear systems whose zero dynamics may be unstable. Under the assumption that the inverse dynamics of the system is stochastic input-to-state stabilizable, a stabilizing output-feedback controller is constructively designed by the integrator backstepping method together with a new reduced-order observer design and the technique of changing supply functions. It is shown that, under small-gain type conditions for small signals, the resulting closed-loop system is globally asymptotically stable in probability. The obtained results extend the existing methodology from deterministic systems to stochastic systems. An example is given to demonstrate the main features and effectiveness of the proposed output-feedback control scheme.     

一类控制系数未知但等同高阶非线性系统的稳定控制设计

本文研究了一类控制系数未知但等同高阶非线性系统的状态反馈稳定控制设计问题. 尽管该类系统具有不确定性, 即控制系数未知,但本文没有采用自适应技术, 而是通过选取适当的设计参数, 从而得到了设计该类非线性系统稳定控制器的新方法, 并基于反推技术, 给出了稳定控制器的设计步骤. 所设计的状态反馈控制器使得闭环系统全局渐近稳定, 并保持在原点的平衡性.     

Linear periodic controller design for decentralized control systems

In the decentralized control of linear time-invariant (LTI) systems, a decentralized fixed mode (DFM) is a system mode which is immoveable using an LTI controller, while a quotient DFM (QDFM) is one which is immoveable using any form of nonlinear time-varying compensation. If a system has no unstable DFMs, there are well-known procedures for designing an LTI stabilizing controller; for systems which have unstable DFMs but no unstable QDFMs, we provide a simple design algorithm which yields a linear periodic sampled-data stabilizing controller.     

基于广义扩张状态观测器的干扰不匹配离散系统状态反馈控制

针对一类干扰不匹配的线性离散时间系统, 研究基于广义扩张状态观测器的稳定化状态反馈控制器设计问题. 在经典的自抗扰控制器中, 扩张状态观测器主要针对干扰匹配的积分串联型系统. 然而, 在许多实际系统中往往存在干扰不匹配的情况, 例如存在采样抖动的离散时间控制系统. 针对这一问题, 基于一类存在不匹配干扰的离散时间系统, 提出广义扩张状态观测器和相应的稳定化状态反馈控制器设计方法. 最后通过永磁同步电机调速控制仿真实例验证了所设计的观测器和控制器的有效性.

     

Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain

We consider a global regulation problem of a class of feedforward nonlinear systems with uncertain delays by output feedback. The considered system is a generalized feedforward time-delay nonlinear system in the sense that an additional uncertain constant delay exists in the main control input to the system and feedforward nonlinearity includes states and input which have uncertain time-varying delays. Moreover, when feedforward nonlinearity satisfies some restrictive condition, we extend our control problem to the case such that the delay in the main control input is also a time-varying delay. To globally regulate the considered system, we develop an output feedback controller whose gain-scaling factor involves an adaptive dynamic. Two examples are given for illustration.     

基于改进主从控制结构的海洋机器人零航速减摇鳍系统

利用零航速减摇鳍系统实现对海洋机器人在近水面低速航行时的横摇姿态控制. 基于零航速减摇鳍的非线 性动态特性和海洋机器人横摇解耦模型, 提出具有主从结构的横摇减摇控制规律. 设计具有积分滑模面的变结构控 制规律, 估算系统期望横摇扶正力矩, 并进一步结合非线性跟踪控制理论和反馈线性化方法, 建立减摇鳍子系统模 型, 设计从属控制规律驱动减摇鳍产生实际横摇稳定力矩. 仿真结果和理论分析表明, 所设计的控制规律是稳定且有 效的.

     

一类不确定非线性系统的输出反馈半全局镇定

研究了一类不确定非线性系统的输出反馈半全局镇定问题. 不同于现有文献,本文研究的控制系统具有更强的非线性和未知控制系数,这增加了设计输出反馈控制器的难度. 基于反推方法和输出反馈占优方法,设计了输出反馈半全局控制器. 通过选取适当的设计参数,该控制器可以保证闭环系统的半全局渐近稳定. 仿真实例验证了理论结果的有效性.     

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems

A new approach for the design of robust H_∞ observers for a class of Lipschitz nonlinear systems with time‐varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time‐varying parametric uncertainties. Explicit norm‐wise and element‐wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H_∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.     

A methodology for designing controllers for industrial systems based on nonlinear separation model and control

A feasible method of controller design for industrial nonlinear dynamic systems is proposed, by separating the nonlinear dynamic system into nonlinear static parts and a linear dynamic part. The proposed method of industrial controller design reduces the existing gaps between the control theory and the actual field. In the controller construction procedure of a system, the nonlinearities are eliminated by using the inversion functions of the nonlinear static parts. Any conventional control theory is ideally applicable to a linear dynamic part of the system. Based on the proposed method of nonlinear separation, controllers were constructed for three different systems: a chemical reactor, a temperature level-controlled tanked water system, and the contour-following control of an articulated robot arm. Some encouraging control performances, superior to those of other existing controllers, showed its significant potential for application to industrial systems with nonlinearities.     

一类不确定非线性系统无过参数自适应控制设计新方法

文中研究了一类控制系数未知的更一般高阶不确定非线性系统的全局稳定自适应控制设计问题.尽管现有文献已解决了该问题,但对于n维系统,现有构造稳定自适应控制的方法至少需要设计n+1个未知参数的动态调节律,即动态补偿器的维数至少为n+1,存在较为严重的过参数问题.文中通过定义新的需动态调节的未知参数,运用增加幂积分和有关自适应技术,成功地解决了已有方法中的过参数问题,给出了构造只含有一个参数调节律的稳定自适应控制设计新方法.仿真算例验证了文中所给方法的有效性.