非线性控制系统的全局输出调节

讨论了非线性控制系统的全局输出调节.首先推广精确线性化方法,通过状态反馈 和微分同胚将非线性系统的全局输出调节问题,转化为线性系统对非线性系统的跟踪问题. 通过提出可解性的概念,得到线性系统对非线性系统全局跟踪的条件,该结果是线性系统结 果的推广.在反馈同胚变换全局成立条件下,得到非线性控制系统全局输出调节问题的充分 条件,该条件对外部系统只做较弱的可解性假设,在反馈同胚变换局部成立的条件下,可得局 部结果.     

非线性控制系统的全局输出调节1)

讨论了非线性控制系统的全局输出调节.首先推广精确线性化方法,通过状态反馈和微分同胚将非线性系统的全局输出调节问题,转化为线性系统对非线性系统的跟踪问题.通过提出可解性的概念,得到线性系统对非线性系统全局跟踪的条件,该结果是线性系统结果的推广.在反馈同胚变换全局成立条件下,得到非线性控制系统全局输出调节问题的充分条件,该条件对外部系统只做较弱的可解性假设,在反馈同胚变换局部成立的条件下,可得局部结果.     

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.     

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.     

非线性大系统的分散输出反馈半全局鲁棒镇定

从半全局镇定角度研究非线性大系统的分散输出反馈鲁棒镇定问题．对一类满足新型增长条件的非线性大系统, 给出了分散输出反馈半全局鲁棒镇定控制器的设计方法．对任意给定状态空间的紧子集, 可经此方法设计分散输出反馈控制器, 使受控大系统在原点是渐近稳定的同时吸引域包含指定的紧子集．     

齐次非线性系统H_∞控制的输出反馈(英文)

研究了齐次系统H∞ 控制的输出反馈问题 .首先给出齐次镇定与二次型Lyapunov函数之间的关系 .随后讨论了齐次系统H∞ 控制的输出反馈问题 .在适当条件下 ,给出了全局解 .然后考虑了具有高阶扰动项的齐次系统 ,对此系统也得到了与无扰动项时的相似结论 .     

一种推广的组合非线性输出反馈控制

针对多变量饱和线性系统的时变参考输入跟踪问题,研究了一种组合非线性输出反馈控制器的设计方法.基于原始的组合非线性反馈理论,构造了全阶和降阶输出反馈控制器.控制器由线性输出反馈项和非线性反馈项组成,使得闭环系统在包含于吸引域的不变集内渐近稳定.除了能够跟踪时变参考输入外,系统还具有良好的动态性能.仿真结果说明了所开发控制器的有效性.     

具有多项式型非线性项的大规模随机非线性系统的分散输出反馈镇定

基于齐次占优方法研究 具有多项式型非线性项的大规模随机非线性系统的分散输出反馈镇定问题. 本文的主要贡献在于利用高增益齐次占优方法来解决大规模随机非线性系统的分散控制问题. 这种方法能彻底地去掉传统结果中所要求的线性增长条件, 不仅推广了以前的结果还得到了一些新的结果. 仿真验证了输出反馈控制器的有效性.     

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.     

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.     

Output feedback stabilization of time‐delay nonlinear systems with unknown continuous time‐varying output function and nonlinear growth rate

This article addresses the problem of global output feedback stabilization for a class of time‐varying delay nonlinear systems with polynomial growth rate. The systems under investigation possess two remarkable features: the output is perturbed by an unknown sensitivity function that is not differentiable but continuous, and the nonlinearities are bounded by a polynomial function of the output multiplied by unmeasurable state variables. The new full‐order observer is established by introducing a dynamic gain and filtering unknown nonlinearities and time‐varying delay. With the help of the transformation skill and the reasonable combination of several systems, this article proposes a linear output feedback controller with the dynamic gain and completes the performance analysis based on the construction of two integral Lyapunov functions. Finally, a simulation example is presented to demonstrate the effectiveness of control strategy.     

Robust output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities

In this paper, we consider the problem of global output feedback stabilization for a class of nonlinear systems whose nonlinearities are assumed to be bounded by both low‐order and high‐order nonlinearities multiplied by a polynomial‐type output‐dependent growth rate. Instead of the previously proposed dual observer, based on the homogeneous domination approach, a new reduced‐order observer is constructed, which greatly simplifies the closed‐loop controller and is able to cover a more general class of nonlinear systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Stability analysis and state feedback stabilization of pendulum-like systems with multiple nonlinearities

This paper addresses the Lagrange stability analysis problem and the state feedback Lagrange stabilization problem for pendulum-like systems with multiple nonlinearities. An existing method for analysing the Lagrange stability of pendulum-like systems with a single nonlinearity is generalized to pendulum-like systems with multiple nonlinearities. Also, a non-degeneracy condition of the existing Lagrange stability criterion is removed and a strict frequency-domain inequality is used instead. To study the state feedback Lagrange stabilization problem, this paper develops an extended strict bounded real lemma for linear systems which are not stable but stabilizable. A sufficient condition for state feedback Lagrange stabilization is proposed in terms of an algebraic Riccati equation with a sign indefinite solution.     

An LMI approach to stabilization of linear discrete-time periodic systems

The problem of stabilization of linear discrete-time periodic systems is considered. LMI based conditions for stabilization via static periodic state feedback as well as via static periodic output feedback are presented. In the case of state feedback, the conditions are necessary and sufficient whereas for output feedback the result is only sufficient as it depends on the particular state-space representation used to describe the system. The problem of quadratic stabilization in the presence of either norm-bounded or polytopic parameter uncertainty is also treated. As an application of the output feedback stabilization technique, we consider the problem of designing a stabilizing (respectively, quadratically stabilizing) static periodic output feedback controller for linear time-invariant discrete-time systems which are not stabilizable (respectively, quadratically stabilizable) by static constant output feedback.     

Output feedback control of large-scale nonlinear time-delay systems in lower triangular form

This paper is concerned with the stabilization problem for a class of large-scale nonlinear time-delay systems in lower triangular form. The uncertain nonlinearities are assumed to be bounded by continuous functions of the outputs or delayed outputs multiplied by unmeasured states or delayed states. An observer based output feedback control scheme is proposed using the dynamic gain control design approach. Based on Lyapunov stability theory, global asymptotic stability of the closed-loop control system is proved. Contrary to many existing control designs for lower triangular nonlinear systems, the celebrated backstepping method is not utilized here. An example is finally given to demonstrate the effectiveness of the proposed design procedure.     

Adaptive tracking and disturbance rejection for uncertain nonlinear systems

This note addresses the problem of asymptotic tracking of arbitrary smooth bounded reference output signals, with simultaneous rejection of disturbances generated by an unknown linear exosystem. The problem is globally solved by output feedback for the class of nonlinear systems with output dependent nonlinearities and unknown linear parameters, under the assumptions that the system is minimum phase and the relative degree, an upper bound on the system order, the sign of the high-frequency gain are known.     

Semi‐Global Output Feedback Stabilization for a Class of Uncertain Nonlinear Systems

This paper addresses the problem of semi‐global stabilization by output feedback for a class of nonlinear systems whose output gains are unknown. For each subsystem, we first design a state compensator and use the compensator states to construct a control law to stabilize the nominal linear system without the perturbing nonlinearities. Then, combining the output feedback domination approach with block‐backstepping scheme, a series of homogeneous output feedback controllers are constructed recursively for each subsystem and the closed‐loop system is rendered semi‐globally asymptotically stable.     

Robust stability of multiple-time-delay uncertain systems with series nonlinearities

This paper considers the problem of output feedback stabilization of multiple time delay uncertain systems with series nonlinearities. We develop a delay-dependent method for designing linear dynamic output feedback controllers which ensures global uniform asymptotic stability for the range of allowable delay times. The proposed stabilization method, which is based on the comparison theorem and some analytical methods, is employed to treat this problem. The most striking feature of the results presented is their simplicity in testing the stabilization of multiple-time-delay systems with series nonlinearities and this can be used to estimate the size of the delay time. Examples are used to illustrate the less conservative results of the proposed methods compared with existing methods in the literature.     

Robust controller synthesis for systems with input nonlinearities: a trade-off between gain variation and parametric uncertainty

A feedback control-system design problem involving input nonlinearities and structured plant parameter uncertainities is considered. Multivariable absolute stability theory is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design that accounts for input time-varying sector bounded nonlinearities. The principal result is a sufficient condition for characterizing dynamic controllers of a fixed dimension which are guaranteed to provide robust stability for plant parametric variations and absolute stabilization for input nonlinearities. The proposed framework provides a systematic design trade-off between classical robustness guarantees (i.e., gain and phase margins) versus parametric robustness. Furthermore, the framework is directly applicable to uncertain systems with saturating controls and provides fixed-order dynamic output feedback controllers with guaranteed domains of attraction. © 1998 John Wiley & Sons, Ltd.     

Robust output feedback stabilization of a class of time-varying non-linear systems

This paper deals with the problem of robust output feedback stabilization of a class of time-varying non-linear systems. This class of systems involves two kinds of time-varying uncertainties: those norm-bounded and those bounded by a smooth non-linear function of the output. Under the assumption that the zero dynamics of the system are uniformly asymptotically stable and some additional mild conditions, we show via a Lyapunov function approach that the uncertain system can be robustly stabilized by a time-varying non-linear output feedback controller. The order of this controller turns out to be one less than the relative degree of the uncertain system. A systematic design procedure is given for constructing the controller. Illustrative examples are given. Note that the results generalize several previous results on robust output feedback stabilization.