具有自适应内模的一类非线性系统输出调节问题

研究一类包含未知非线性项的非线性系统的鲁棒输出调节问题.此类非线性系统由一包含未知参数的线性中性稳定的外系统驱动.首先运用调节器方程组解和标准内模将输出调节问题转化为镇定问题,然后给出控制律镇定闭环系统,同时利用镇定输入项和外系统信息设计出自适应内模方程.控制律使得闭环系统的信号全局最终有界,且误差被调节至预先设定的任意小的精度值.仿真结果验证了所提出设计方法的有效性.

     

一类非线性输出反馈系统的自适应输出调节问题

本文讨论一类非线性系统的全局鲁棒输出调节问题.假定被控非线性系统的系统输入方向未知,且产生参考或扰动信号的外部系统含未知参数,这为控制律的设计带来了挑战.文章使用自适应控制方法和内模原理,解决了一类相对阶为1的非线性输出反馈系统的输出调节问题,并将结果应用于处理Lorenz系统的渐近跟踪问题.     

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.     

基于双增益方法的不确定非线性系统的输出反馈调节问题

研究一类具有多种不确定性的非线性系统的全局输出反馈调节问题.所研究系统的一个显著特点是非线性项被未知增长率和多项式形式的输出函数的乘积界定,难点是在输出受不确定参数摄动的情况下如何抑制非线性项.提出一种改进的双增益方法来设计输出反馈控制器,可以确保闭环系统所有信号全局一致有界并且原系统状态收敛到零.最后,采用质量弹簧机械系统的输出反馈镇定问题来说明控制策略的有效性.     

具有参数不确定性的非线性系统的鲁棒输出跟踪

研究具有非线性参数化的非线性系统的输出跟踪问题.采用时变状态反馈控制律, 指数镇定输出跟踪误差,并保证非线性系统的所有状态是有界的.为了实现时变状态反馈控 制律,设计高增益鲁棒观测器观测构造该控制律所需要的状态,使得整个闭环系统的输出能 渐近跟踪期望输出,且该闭环系统中所有信号都是有界的.     

一类非线性系统的自适应抗测量噪声的输出反馈镇定

本文研究一类非线性系统的自适应抗测量噪声的输出反馈镇定问题. 所研究的非线性系统输出中存在正的且 有界的乘性噪声. 非线性项的增长率为一个未知常数乘以输出的幂函数加上带有时滞输出的幂函数. 首先, 证明一个矩 阵不等式. 其次, 设计含有3个时变增益的输出反馈控制器, 并给出增益的自适应律, 然后, 构造适当的Lyapunov-Krasovskii 泛函, 给出确保闭环系统渐近稳定的充分条件. 最后, 仿真实验验证该方法的可行性和有效性.     

含有不灵敏区非线性系统的增益调度自适应变结构控制

针对具有控制输入不灵敏区及有界不确定性的非线性系统,采用增益调度变结构控制策略,研究其镇定问题.利用增益调度策略和自适应参数估计方法,在同时存在参数、结构及干扰的不确定性和未知控制输入不灵敏区的情形下,提出了新的增益调度自适应变结构镇定控制律设计方法,既节省了控制能量,又消除了控制信号的颤振.所提出的控制律可以保证闭环输出为一致终结有界,并且算法比较简单,便于实现.用数字仿真方法验证了所得控制律设计方法的有效性.     

一类未知参数非线性系统的自适应无源控制

对一类含有未知参数的本质非线性系统,通常的Backstepping方法无法应用.为此,提出一种基于状态反馈的自适应无源控制对策,通过对非线性系统进行反馈无源化控制,设计自适应无源镇定控制器和自适应无源输出跟踪控制器.设计中适当调节自适应无源控制器参数,能够保证闭环系统稳定且所有信号全局一致有界,从而解决了此类含有未知参数非线性系统的稳定性和输出跟踪问题.仿真算例验证了提出控制方案的有效性,表明系统具有较强的稳定性和跟踪特性.     

一类非线性系统的自适应鲁棒输出反馈镇定

讨论了一类不确定非线性系统的鲁棒输出反馈镇定问题,其不确定性是部分已知 的.文中所得连续自适应鲁棒输出反馈控制器确保闭环系统终极一致有界.与已有文献结果 相比,关于未知参数估计的自适应律是连续的,而且闭环系统解的存在性在通常情况下能被 保证.进而,由于输出反馈控制器和自适应律的连续性,使得自适应鲁棒输出反馈控制器在 实际控制问题中易于实现,且使系统具有良好的品质.最后,通过数值算例进一步说明该文 的设计方案是有效的.     

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.     

Semi‐Global Robust Output Regulation for A Class of Singular Nonlinear Systems with Unknown Algebraic Equations

This paper considers semi‐global robust output regulation problem for a class of singular nonlinear systems whose algebraic equations are not precisely known. Since the algebraic equations are not known, the output regulation problem of singular nonlinear systems cannot be solved by directly reducing the singular nonlinear system into a normal nonlinear system. Based on internal model principle, we convert the robust output regulation problem of singular nonlinear systems into a robust stabilization problem of an augmented singular nonlinear system. The augmented singular nonlinear system is also with unknown algebraic equations. However, without transforming the singular nonlinear system into a normal nonlinear system, it is shown that the augmented singular nonlinear system can be semi‐globally stabilized by a high gain output feedback control law under some reasonable assumptions. Moreover, the semi‐global stabilization control law of the augmented singular nonlinear systems also solves the semi‐global robust output regulation problem of the original singular nonlinear system.     

Output regulation for a class of uncertain nonlinear systems with nonlinear exosystems and its application

In this paper, we consider the global robust output regulation problem for a class of uncertain nonlinear systems with nonlinear exosystems. By employing the internal model approach, we show that this problem boils down to a global robust stabilization problem of a time-varying nonlinear system in lower triangular form, the solution of which will lead to the solution of the global robust output regulation problem. An example shows the effectiveness of the proposed approach.     

New results on robust output regulation of nonlinear systems with a nonlinear exosystem

The global robust output regulation problem for nonlinear plants subject to nonlinear exosystems has been a challenging problem and has not been well addressed. The main difficulty lies in finding a suitable internal model. The existing internal model for handling the nonlinear exosystem is not zero input globally asymptotically stable, and can only guarantee a local solution for the output regulation problem. In this paper, we first propose a new class of internal models, which is guaranteed to exist under the generalized immersion condition. An advantage of this internal model is that it is zero input globally asymptotically stable. This fact will greatly facilitate the global stabilization of the augmented system associated with the given plant and the internal model. Then we will further utilize this class of internal models to solve the global robust output regulation problem for output feedback systems with a nonlinear exosystem. Copyright © 2011 John Wiley & Sons, Ltd.     

Output regulation of nonlinear output feedback systems with exponential parameter convergence

This paper revisits the global robust output regulation (GROR) problem of nonlinear output feedback systems with uncertain exosystems by error output feedback control. The problem was conventionally tackled by employing a linear canonical internal model and as a result, suitable adaptive stabilization has to be done for the augmented system to achieve output regulation. Distinguished from that, a novel nonlinear internal model approach is developed in the present study that successfully converts the GROR problem into a robust non-adaptive stabilization problem for the augmented system. The feature of the new approach is two-fold. On one hand, stabilization of augmented system is disentangled from any extra adaptive control law and thus the procedure is simplified. On the other hand, it leads to explicit strict Lyapunov characterization for the closed-loop system and consequently assures exponential parameter convergence.     

Global robust output regulation of lower triangular systems with nonlinear exosystems and its application

This paper studies the global robust output regulation problem for lower triangular systems subject to nonlinear exosystems. By employing the internal model approach, this problem can be boiled down to a global robust stabilization problem of a time-varying nonlinear system in the cascade-connected form. Then, a set of sufficient conditions for the solvability of the problem is derived, and thus, leading to the solution to the global robust output regulation problem. An application of the main result of this paper is also proposed.     

Robust output regulation for discrete‐time nonlinear systems

In this paper, we will establish a framework that can convert the robust output regulation problem for discrete‐time nonlinear systems into a robust stabilization problem for an appropriately augmented system consisting of the given plant and a specific dynamic system called internal model. We then apply this framework to solve the local robust output regulation problem for a general class of discrete‐time nonlinear systems. The results of this paper gives a discrete‐time counterpart of the recent results on the continuous‐time robust output regulation problem. Copyright © 2005 John Wiley & Sons, Ltd.     

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

Most of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.     

Cooperative semi-global robust output regulation for a class of nonlinear uncertain multi-agent systems

In this paper, we study the cooperative semi-global robust output regulation problem for a class of minimum phase nonlinear uncertain multi-agent systems. This problem is a generalization of the leader-following tracking problem in the sense that it further addresses such issues as disturbance rejection, robustness with respect to parameter uncertainties. To solve this problem, we first introduce a type of distributed internal model that converts the cooperative semi-global robust output regulation problem into a cooperative semi-global robust stabilization problem of the so-called augmented system. We then solve the semi-global stabilization problem via distributed dynamic output control law by utilizing and combining a block semi-global backstepping technique, a simultaneous high gain feedback control technique, and a distributed high gain observer technique.     

Global Robust Output Regulation for a Class of Switched Nonlinear Systems with Nonlinear Exosystems

The problem of global robust output regulation for a class of switched nonlinear systems with nonlinear exosystems is investigated in this paper where not all subsystems are stabilizable. First, as an extension of the concept of non‐switched internal model, this paper defines a switched internal model, which together with the plant is called the switched augmented system. Also, we show that the problem of output regulation for the switched nonlinear system can be converted into a global robust regulation problem of the switched augmented system. Second, based on the average dwell time method, the global robust regulation problem under a class of switching signals with average dwell time is solved, which leads to the solution of the problem of global robust output regulation. Finally, an example is provided to demonstrate the effectiveness of the proposed design approach.     

Global robust practical output regulation for nonlinear systems in output feedback form by output‐based event‐triggered control

In this paper, we study the event‐triggered global robust practical output regulation problem for a class of nonlinear systems in output feedback form with any relative degree. Our approach consists of the following three steps. First, we design an internal model and an observer to form the so‐called extended augmented system. Second, we convert the original problem into the event‐triggered global robust practical stabilization problem of the extended augmented system. Third, we design an output‐based event‐triggered control law and a Zeno‐free output‐based event‐triggered mechanism to solve the stabilization problem, which, in turn, leads to the solvability of the original problem. Finally, we apply our result to the controlled hyperchaotic Lorenz systems.