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.  

Global practical tracking of a class of nonlinear systems by output feedback

In this paper we address the practical tracking problem for a class of nonlinear systems by dynamic output feedback control. Unlike most of the existing results where the unmeasurable states in the nonlinear vector field can only grow linearly, we allow higher-order growth of unmeasurable states. The proposed controller makes the tracking error arbitrarily small and demonstrates nice properties such as robustness to disturbances and universal property to reference signals.  

一类具有未知增长率非线性系统全局输出反馈实际跟踪

本文研究了一类仅跟踪误差可量测不确定非线性系统的全局输出反馈实际跟踪问题.不同于现有文献,该控制系统具有依赖于不可测状态的增长且增长率为未知常数,并且只要求被跟踪信号及其一阶导数有未知界,因此直接推广现有结果难以解决上述控制问题.受相关镇定结果的启发,并通过灵活运用广义控制(universal control)和死区(dead zone)的方法与技巧,本文设计了自适应输出反馈控制器.主要结果表明,所设计的控制器能够确保跟踪误差经有限时间后收敛于设定的原点的任意小邻域,同时闭环系统的所有信号皆有界.仿真算例验证了理论结果的有效性.  

Global Practical Tracking for Nonlinear Systems With More Unknowns via Adaptive Output‐Feedback

This paper investigates the global practical tracking via adaptive output‐feedback for a class of uncertain nonlinear systems. Essentially different from the closely related literature, the system under investigation possesses unknown time‐varying control coefficients and a polynomial‐of‐output growth rate, and meanwhile, the system nonlinearities and the reference signal allow serious unknowns. For this, an adaptive observer is designed to reconstruct the system unmeasured states, where a new dynamic gain is introduced to compensate the serious unknowns in the system nonlinearities and the reference signal. Based on this and by backstepping technique, an adaptive output‐feedback controller is successfully designed, such that all the states of the closed‐loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical simulation is provided to demonstrate the effectiveness of the proposed 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.  

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.  

Global practical tracking of a class of nonlinear systems using linear sampled-data control

This paper considers the problem of global practical tracking via sampled-data control for a class of uncertain nonlinear systems. Under a lower triangular linear growth condition, a sampled-data state feedback controller is first constructed such that the states are globally bounded and the error between the system output and the reference signal will be rendered smaller than a given tolerance. When only the output of the system is measurable, a sampled-data output feedback controller, whose observer and control law are both linear, is constructed to solve the global practical tracking problem.  

Global tracking sliding mode control for a class of nonlinear systems via variable gain observer

A novel output‐feedback sliding mode control strategy is proposed for a class of single‐input single‐output (SISO) uncertain time‐varying nonlinear systems for which a norm state estimator can be implemented. Such a class encompasses minimum‐phase systems with nonlinearities affinely norm bounded by unmeasured states with growth rate depending nonlinearly on the measured system output and on the internal states related with the zero‐dynamics. The sliding surface is generated by using the state of a high gain observer (HGO) whereas a peaking free control amplitude is obtained via a norm observer. In contrast to the existing semi‐global sliding mode control solutions available in the literature for the class of plants considered here, the proposed scheme is free of peaking and achieves global tracking with respect to a small residual set. The key idea is to design a time‐varying HGO gain implementable from measurable signals. Copyright © 2010 John Wiley & Sons, Ltd.