增长率为输出的未知多项式非线性系统的全局输出反馈跟踪

本文研究了一类增长线性地依赖于不可测状态非线性系统的输出反馈自适应实用跟踪问题.很不同的是,本文所研究系统的增长率是输出的未知多项式(系数未知、幂次已知),且关于被跟踪参考信号的假设相当弱(仅本身和其导数为已知的),为解决该问题,通过灵活采用通用控制和死区的思想和方法,引入了带有新型动态增益的观测器来重构不可测的系统状态,进而构造了自适应输出反馈跟踪控制器.可以证明,当控制器中的设计参数适当选取时,闭环系统所有状态有界,并且跟踪误差趋于事先给定的充分小的区域.数值仿真说明了所提方法的有效性.     

一类不确定非线性系统自适应输出反馈跟踪控制的新结果

研究了一类不确定非线性系统的自适应输出反馈实际跟踪控制问题. 解决该控制问题的困难主要源于此类系统控制系数不确定, 并具有依赖于不可测状态的增长且其增速是关于输出的多项式函数. 首先, 通过推广现有的K–滤波器, 引入了新的动态高增益K–滤波器, 并基于此构造了状态观测器. 然后, 应用反推技术, 成功的设计了系统的自适应输出反馈跟踪控制器. 主要结果表明, 通过设计参数的适当选择, 所构造的控制器能保证闭环系统的所有状态全局有界, 并且当时间足够大时, 跟踪误差收敛到零点的既定小邻域内.     

一类增长率依赖输出的非线性系统的输出反馈输出跟踪控制

研究一类增长率依赖输出非线性系统的输出反馈输出跟踪控制问题.利用系统结构特点,构造出系统实现输出跟踪时内部状态的渐近轨迹.通过建立状态与渐近轨迹偏差的动态方程,将输出跟踪问题转化为偏差系统的镇定问题,然后通过设计偏差系统的输出反馈镇定控制器给出输出反馈输出跟踪控制器.最后以仿真实例验证本文结论.     

基于神经网络的一类非线性系统自适应输出跟踪

针对一类未知非线性系统,提出了一种输出反馈控制方法.首先,在假设系统状态已知情况下设计状态反馈控制器,实现跟踪性能;然后,在系统状态不完全可测的情况下,通过设计高增益观测器对系统的状态进行估计,实现输出反馈控制器设计,证明了所设计的输出反馈控制器可以获得状态反馈控制器的性能.     

一类不确定非线性系统的指数鲁棒输出跟踪

研究一类不确定非线性系统的鲁棒输出跟踪控制问题。应用输入／输出反馈线性化法和李亚普诺夫方法,提出一种基于不确定项上界的连续型鲁棒输出跟踪控制器设计方法。该控制器不仅可确保闭环系统的状态一致最终有界,使系统输出按指数规律跟踪期望输出,而且计算简单,更易实现。仿真结果证明了该方法的可行性与有效性。     

一类非线性系统输出反馈的半全局实用镇定

研究了一类含有未知参数的非线性系统的半全局实用镇定问题,通过系统线性部分和零动态部分的Lyapunov函数构造了整个系统的Lyapunov函数,据此设计了使系统半全局实用稳定的状态反馈和动态输出反馈,且证明了只要未知参数不改变系统的相对阶,那么控制器是鲁棒的.仿真实例说明了所提出方法的有效性.     

一类带不确定输入动态非线性系统的输出反馈鲁棒镇定

研究一类带不确定输入动态非线性系统的输出反馈鲁棒镇定问题.通过在高增益观测器引入新的设计参数,改进了通常的高增益反馈控制的设计方法.在输入动态满足零相对阶最小相位的假设下,基于非分离设计原则给出了动态输出反馈控制器的设计方法,所设计的控制器实现了对任意可允许不确定输入动态的全局鲁棒镇定.     

一类不确定非线性系统的自适应输出反馈镇定

研究了一类不确定非线性系统的全局自适应输出反馈镇定问题. 由于不确定控制系数和未知线性增长率的存在, 这个问题比较复杂且很难解决. 本文引入一个新的在线调节的动态增益, 并基于此设计了高增益K-滤波器用于重构系统的状态. 然后, 受广义控制方法的启发, 发展了反推法并设计了自适应输出反馈镇定控制器. 结果表明, 通过选择恰当的设计参数可以保证闭环系统的全局稳定性. 给出的仿真算例验证了本文理论结果的正确性.     

一类具有未知控制方向非线性系统的输出反馈自适应控制

研究了一类控制方向未知非线性系统的输出反馈自适应镇定问题. 首先, 通过一线性状态变换, 将未知控制系数集中起来, 从而将原系统变换为适于控制设计的新系统. 然后, 分别引入状态观测器和参数估计器, 并应用积分反推和调节函数方法, 给出了输出反馈稳定控制律的构造性设计过程. 可以证明,所设计的控制器确保原系统状态渐近收敛到原点, 而其它闭环系统状态有界. 仿真结论验证了所提出方法的有效性.     

一类非线性系统的间接自适应输出反馈模糊控制

针对一类未知非线性系统,提出一种输出反馈控制方法。首先在假设系统状态已知的情况下设计状态反馈控制器,实现跟踪性能。然后在系统状态不完全可测的情况下,通过设计高增益观测器对系统的状态进行估计,实现输出反馈控制器设计。最后证明所设计的输出反馈控制器可获得状态反馈控制器所取得的最大最小问题的跟踪性能。     

Global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and unmeasured states dependent growth

This paper considers the problem of global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and with unmeasured states dependent growth. Mainly due to the uncertain control coefficients, the problem has remained unsolved and its major difficulty stems from the inapplicability of the commonly used high-gain like observer. By introducing an appropriate state transformation and a thoroughly novel observer based on high-gain K-filters, the backstepping design approach is successfully proposed to the output-feedback controller for this class of systems. It is shown that the global asymptotic stability of the closed-loop system can be guaranteed by the appropriate choice of the control parameters.     

Adaptive practical output tracking control for a class of uncertain nonlinear systems

This paper investigates the problem of adaptive practical tracking control by output feedback for a class of uncertain nonlinear systems without zero dynamics. The uncertain nonlinear perturbed terms of the considered systems are assumed to satisfy a generalised condition which is more relaxed than the triangular-type condition. Furthermore, in contrast to the previous work in the literature, the upper bound of the nonlinearities is a polynomial function of the output, with an unknown growth rate, multiplied by some relaxed conditions of unmeasured states. Due to the presence of unknown parametric uncertainty, a dynamic output compensator with dynamically updated gains is explicitly constructed based on non-separation principle. In particular, we show that for any positive number γ, all the states of the closed-loop systems are globally bounded and the tracking error belongs to the interval [?γ, γ] after some positive finite time. A numerical example illustrates the efficiency of the method.     

Adaptive output‐feedback tracking for nonlinear systems with rather general control coefficients

This paper studies the problem of global practical tracking by output feedback for a class of uncertain nonlinear systems with unmeasured state‐dependent growth and unknown time‐varying control coefficients. Compared with the closely related works, the remarkableness of this paper is that the upper and lower bounds of unknown control coefficients are not required to be known a priori. Motivated by our recent works, by combining the methods of universal control and deadzone with the backstepping technique and skillfully constructing a novel Lyapunov function, we propose a new adaptive tracking control scheme with appropriate design parameters. The new scheme guarantees that the state of the resulting closed‐loop system is globally bounded while the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. Two examples, including a practical example, are given to illustrate the effectiveness of the theoretical results.     

Further results on global practical tracking via adaptive output feedback for uncertain nonlinear systems

This paper is concerned with the global practical tracking via adaptive output feedback for a class of uncertain nonlinear systems. The system under investigation possesses function control coefficients, the polynomial-of-output growth rate and serious unknowns in the system nonlinearities and the reference signal, and hence is essentially different from those in the closely related literature. To solve the problem, a high-gain observer is introduced to reconstruct the unmeasured system states. The involved high gain is the multiplication of two dynamic gains: one is to compensate the polynomial-of-output in the system growth rate, and the other one is to overcome the serious unknowns in the system and reference signal and the extra system nonlinearities in function control coefficients. Based on the high-gain observer, an adaptive output-feedback controller is successfully designed to guarantee that, for any initial condition of the system, all signals of the closed-loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical example demonstrates the effectiveness of the proposed method.     

Global adaptive tracking for a class of nonlinear time-delay systems

This paper aims to extend the newly developed global adaptive regulation scheme to adaptive tracking for a general class of nonlinear systems with both parameter uncertainties and unknown time delay for all the system states. With a simple yet novel decomposition of some coupling functions derived from the introduction of a reference signal, a backstepping tracking control strategy is proposed which possesses the feature that for each design step, a dynamic gain is introduced to generate an additional term to counteract the system nonlinearities and parameter uncertainties. As a result, a memoryless adaptive state-feedback controller is obtained to achieve the global adaptive tracking.     

Global stabilisation via switching output-feedback for power integrator systems with unknown control direction

This paper considers the global output-feedback stabilisation for power integrator systems with unknown control direction. The presence of uncontrollable and unobservable linearisation renders the strategy based on Nussbaum function rather difficult (even impossible) to compensate the unknown control direction. In this paper, to dominate the inherent nonlinearities and unknowns, a powerful switching strategy is proposed by combining an output-feedback scheme and a switching mechanism. First, a special case with known control direction is considered to provide a basic structure and selection rules of design parameters for the expected controller, and then, the essential case with unknown control direction is investigated to build a suitable switching logic to online tune the design parameters. The proposed switching-type output-feedback controller guarantees that all the system signals are globally bounded and ultimately converge to zero. A numerical example is given to illustrate the effectiveness of the proposed methods.     

Robust adaptive tracking of uncertain nonlinear systems by output feedback

We investigate the problem of robust adaptive tracking by output feedback for a class of uncertain nonlinear systems. Based on the high‐gain scaling technique and a new adaptive law, a linear‐like output feedback controller is constructed. Only one dynamic gain is designed, which makes the controller easier to implement. Furthermore, by modifying the update law, the adaptive controller is robust to bounded external disturbance and is able to guarantee the convergence of the output tracking error to an arbitrarily small residual set. A numerical example is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.