具有零动态仿射非线性系统控制Lyapunov函数的构造

研究具有零动态仿射非线性系统控制Lyapunov函数的构造问题.提出通过求解一个Lyapunov方程获得可线性化部分的二次型控制Lyapunov函数.由可线性部分的控制Lyapunov函数和零动态部分的Lyapunov函数,通过构造一个正定函数,得到了整个系统的控制Lyapunov函数,且设计了可半全局镇定整个闭环系统的控制律.仿真实例说明了所提出方法的有效性.     

基于鲁棒控制Lyapunov 函数的非线性预测控制

针对一类约束不确定性非线性仿射系统,提出一种可保证闭环系统鲁棒镇定的非线性模型预测控制算法.利用鲁棒控制Lyapunov函数得到改进的Sontag公式,并以此为基础,构造一种计算有效的单自由度鲁棒预测控制器.以Matlab语言为仿真工具,对一开环不稳定振荡器进行了仿真研究,结果表明,利用该控制算法得到的闭环系统不仅渐近稳定于原点,而且所得控制量和系统状态都满足系统约束,从而验证了控制算法的有效性.     

基于量化依赖Lyapunov函数的有界丢包网络控制系统的保成本控制

研究了一类具有有界丢包的网络控制系统（Networked control systems,NCSs）的保成本控制问题,提出了一种包含量化反馈的网络控制系统数学模型,该模型将系统的镇定问题转化为镇定一系列子系统的鲁棒控制问题.在对网络控制系统的分析中,区别于常用的二次型Lyapunov函数,本文采用了一种新的且能够降低保守性的量化依赖Lyapunov函数方法.基于本文的Lyapunov函数,得到了充分考虑丢包过程的保成本控制器的设计方法.仿真算例验证了所给出方法的有效性.     

具有状态和控制滞后的 线性时变时滞系统的输出反馈镇定

研究具有状态和控制滞后的线性时变时滞系统的静态输出反馈镇定，其设计过程只需解一个特殊的代数Ｒｉｃｃａｔｉ方程。并且指出，系统的动态输出反馈镇定问题可等价为广义系统的静态输出反馈镇定问题。最后通过实例论证了本方法的有效性。     

带有未知参数的惯性轮摆系统的自适应控制

针对带有未知参数的惯性轮摆系统,提出了一种自适应控制律设计方法。首先利用坐标变换将惯性轮摆系统的动力学模型转化为级联系统的形式。然后,针对系统参数未知的问题,在已有的惯性轮摆系统反馈控制律的基础上,利用控制器迭代设计思想,设计了惯性轮摆系统的自适应控制律,并利用李雅普诺夫稳定性理论证明了所得自适应控制律可以使得带有未知参数的惯性轮摆系统保持在摆杆垂直向上的平衡状态。最后以一个实际的惯性轮摆系统为例,采用该系统的物理参数进行仿真,分析了不同自适应参数下惯性轮摆系统各状态的收敛速度及摆起和稳定时间。仿真结果验证了所设计自适应控制器能够使惯性轮摆系统从垂直向下的平衡位置摆起并稳定在垂直向上的平衡位置。     

一类线性切换系统的鲁棒状态反馈镇定

考虑一类标称系统存在共同Lyapunov函数的切换系统的鲁棒镇定问题。在不确定性不满足匹配条件下,设计出鲁棒状态反馈控制器,并在给定的切换策略下,确保闭环系统在其平衡点处渐近稳定。仿真结果表明所设计控制器是有效的。     

结构不确定性线性多变量系统鲁棒控制*

本文回顾了结构不确定性线性多变量系统鲁棒控制的分析与设计中,过去与近来对系统稳定鲁棒和性能优化方面的进展。无论对于频域描述研究的方法,还是对于时域描述研究的结果,本文均加以讨论与评价。本文还着重讨论了很有前途的结构不确定性线性多变量系统鲁棒控制的H~∞与μ方法,并探讨了将来的研究方向。     

采用多Lyapunov函数的混杂系统稳定性研究

针对一类由离散事件监控的连续动态子系统组成的混杂动态系统, 首先分析利用多Lyapunov函数方法已有成果, 指出切换超平面为滑动模时, 利用这种方法不能确保混杂系统的稳定. 基于Filipov理论给出了能活稳定性结果. 对于混杂系统的连续动态子系统为线性时不变情况下, 研究了混杂系统二次镇定条件. 最后给出一个例子来说明本文方法.     

基于障碍Lyapunov 函数的输出有界全局收敛鲁棒控制

为了克服基于障碍Lyapunov函数反演控制方法在输出约束控制中约束变量收敛区间小和要求模型精确已知的缺陷,提出一种输出有界且全局收敛的鲁棒控制策略。将收敛区间扩展到全局,并使输出保持在约束区间内;同时消除了由未知干扰和模型不确定性引起的稳态误差,放宽了对指令信号连续可导的限制。应用于电动舵机位置伺服控制的仿真结果表明,舵面能够全局稳定且摆幅有界,稳态无静差,动态响应快,抗扰动能力强。     

多重线性单输入系统的同时镇定

本文研究了多重单输入系统的同时状态反馈镇定问题，证明了r 1个单输入系统的同时镇空问题等价于r个系统用一个Hurwitz反馈向量同时镇定的问题，并对2个系统的情况给出了一个设计的例子。     

Asymptotic feedback stabilization: A sufficient condition for the existence of control Lyapunov functions

In this paper we study the feedback stabilization problem for a wide class of nonlinear systems that are affine in the control. We offer sufficient conditions for the existence of ‘Control Lyapunov functions’ that according to [3,23] and [28–30] guarantee stabilization at a specified equilibrium by means of a feedback law, which is smooth except possibly at the equilibrium. We note that the results of the paper present a local nature.     

Further remarks on strict input-to-state stable Lyapunov functions for time-varying systems

We study the stability properties of a class of time-varying non-linear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our given Lyapunov functions which guarantee the existence of strict ISS Lyapunov functions for our systems. Next, we provide simple direct constructions of explicit strict ISS Lyapunov functions for our systems by applying an integral smoothing method. We illustrate our constructions using a tracking problem for a rotating rigid body.     

Lyapunov functions for the multivariable Popov criterion with indefinite multipliers

We demonstrate the existence of Lur’e-Postnikov type Lyapunov functions for a reasonably general form of the multivariable Popov criterion. In particular, the multipliers need not be positive semi-definite. We discuss the application to the special cases where the feedback element is either diagonal, unstructured or linear.     

On linear co-positive Lyapunov functions for sets of linear positive systems

In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of “linear” stability for the arbitrary switching case; namely, the existence of such a linear Lyapunov function can be related to the requirement that a number of extreme systems are Metzler and Hurwitz stable. Examples are given to illustrate the implications of our results.     

Construction of control Lyapunov functions for damping stabilization of control affine systems

This paper considers the stabilization of nonlinear control affine systems that satisfy Jurdjevic–Quinn conditions. We first obtain a differential one-form associated to the system by taking the interior product of a non vanishing two-form with respect to the drift vector field. We then construct a homotopy operator on a star-shaped region centered at a desired equilibrium point that decomposes the system into an exact part and an anti-exact one. Integrating the exact one-form, we obtain a locally-defined dissipative potential that is used to generate the damping feedback controller. Applying the same decomposition approach on the entire control affine system under damping feedback, we compute a control Lyapunov function for the closed-loop system. Under Jurdjevic–Quinn conditions, it is shown that the obtained damping feedback is locally stabilizing the system to the desired equilibrium point provided that it is the maximal invariant set for the controlled dynamics. The technique is also applied to construct damping feedback controllers for the stabilization of periodic orbits. Examples are presented to illustrate the proposed method.     

Strict Lyapunov functions for time-varying systems

Uniformly asymptotically stable periodic time-varying systems for which is known a Lyapunov function with a derivative along the trajectories non-positive and negative definite in the state variable on non-empty open intervals of the time are considered. For these systems, strict Lyapunov functions are constructed.     

Output feedback control of switched nonlinear systems using multiple Lyapunov functions

This work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of “lower-level” bounded nonlinear feedback controllers together with “upper-level” switching laws that orchestrate the transitions between the constituent modes and their respective controllers. Both the state and output feedback control problems are addressed. Under the assumption of availability of full state measurements, a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding stability region for each mode. A set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed-loop system. When complete state measurements are unavailable, a family of output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high-gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain. A different set of switching rules, based on the evolution of the state estimates generated by the observers, is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes. The differences between the state and output feedback switching strategies, and their implications for the switching logic, are discussed and a chemical process example is used to demonstrate the proposed approach.     

Stabilizability of switched linear systems does not imply the existence of convex Lyapunov functions

Counterexamples are given which show that a linear switched system (with controlled switching) that can be stabilized by means of a suitable switching law does not necessarily admit a convex Lyapunov function. Both continuous- and discrete-time cases are considered. This fact contributes in focusing the difficulties encountered so far in the theory of stabilization of switched system. In particular the result is in contrast with the case of uncontrolled switching in which it is known that if a system is stable under arbitrary switching then admits a polyhedral norm as a Lyapunov function.     

Max-type copositive Lyapunov functions for switching positive linear systems

The paper aims to expand the stability analysis framework based on copositive Lyapunov functions (CLFs) for arbitrarily switching positive systems with continuous- or discrete-time dynamics. The first part focuses on max-type CLFs. It provides an algebraic characterization (in terms of weak quasi-linear inequalities), as well as an existence criterion relying on a concrete construction procedure (in terms of Perron–Frobenius eigenstructure). The second part explores the connections between max-type and two other classes of CLFs, namely linear and quadratic-diagonal. New qualitative and quantitative features are revealed for the CLFs belonging to the two mentioned classes.