Constructive stabilization for quadratic input nonlinear systems

In this paper stabilization of nonlinear systems with quadratic multi-input is considered. With the help of control Lyapunov function (CLF), a constructive parameterization of controls that globally asymptotically stabilize the system is proposed. Two different cases are considered. Firstly, under certain regularity assumptions, the feasible control set is parameterized, and continuous feedback stabilizing controls are designed. Then for the general case, piecewise continuous stabilizing controls are proposed. The design procedure can also be used to verify whether a candidate CLF is indeed a CLF. Several illustrative examples are presented as well.     

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities(LMIs).     

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities （LMIs）.     

一类不确定时滞系统的自适应控制

设计基于观测器的自适应控制器,利用Lyapunov稳定性理论分析系统的稳定性,得到利用线性矩阵不等式表示的闭环系统稳定的充分条件,观测增益矩阵和反馈增益矩阵可以通过求解线性矩阵不等式得到。通过一个实例验证所给结论的有效性。     

Anti-windup design with guaranteed regions of stability for discrete-time linear systems

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be locally modeled by a linear system with a deadzone nonlinearity. Then, based on the use of a new sector condition and quadratic Lyapunov functions, stability conditions in an LMI form are stated. These conditions are then considered in a convex optimization problem in order to compute an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system. Moreover, considering asymptotically stable open-loop systems, it is shown that the conditions can be slightly modified in order to determine an anti-windup gain that ensures global stability. An extension of the proposed results to the case of dynamic anti-windup synthesis is also presented in the paper.     

Stabilization for a class of stochastic nonlinear systems with arbitrary switching via the common Lyapunov function method

This paper addresses the stabilization problem for a class of stochastic nonlinear systems with arbitrary switching. Based on the simultaneous domination approach, the common Lyapunov function method and the backstepping technique, a state feedback controller and an output feedback controller are designed, respectively. The closed-loop systems are proved to be globally asymptotically stable in probability. The main advantage of the proposed control schemes is that the controllers are independent of switching signal. Two simulation examples are given to illustrate the effectiveness of the proposed control strategies.     

线性不确定系统具有完整性的一种设计方法

研究了参数不确定状态反馈控制系统的鲁棒容错问题,目的是设计状态反馈控制器使得对可容许的参数不确定性及传感器失效故障或／和执行器失效故障,系统依然保持全局渐近稳定,具有完整性。基于Lyapunov稳定性理论,应用矩阵的谱半径和最小特征值等概念,分别针对传感器失效、执行器失效以及传感器和执行器同时失效三种情况,推导出使闭环系统渐近稳定的三个定理,给出了一种新的、简单的控制律设计方法和设计步骤。最后,给出了一个设计算例,并就各种可能的传感器或／和执行器失效故障情况进行了仿真分析,应用研究结果验证了所提出方法的有效性和简单性。     

轧机速度系统积分反步控制器的研究

本文给出了轧机速度系统的积分反步控制器设计方法,此方法通过逐步修正算法设计镇定控制器,实现系统的全局调节或跟踪．在每一步把状态坐标变换和一个已知Lyapunov函数的虚拟控制系统的镇定函数等联系起来,最终得到一个控制李稚普诺夫函数(clf).然后．基于上述方法设计了直流电机驱动的轧机速度系统非线性反馈控制器,用来说明积分反步法也适用于线性系统、仿真研究结果表明．本文所设计的反馈控制器使闭环系统稳定,且使系统具有良好的跟踪性能。     

离散Markov跳变系统事件触发H∞量化输出反馈控制

主要研究了基于事件触发机制的离散Markov跳变系统的量化H∞输出反馈控制问题,对系统的建模、稳定性分析、控制器设计等三个方面进行了研究。首先,提出了事件触发通信机制来确定当前采样数据是否能够传输到控制器当中。其次,在传感器与控制器之间引入对数量化器,利用扇形有界方法,量化采样数据达到降低网络中的数据传输速率的目的。接下来,考虑网络诱导时延建立一种具有外部扰动的Markov跳变时滞系统。构造Lyapunov-Krasovskii 泛函,得到使闭环系统渐近稳定且满足H∞性能指标的充分条件,在此基础上设计相应的输出反馈控制器。最后通过数值仿真来证明本文所提方法的有效性。     

Controller switching based on output prediction errors

We consider a switched nonlinear feedback control strategy for controlling a plant with unknown parameters so that the output asymptotically tracks a reference signal. The controller is selected online from a given set of controllers according to a switching rule based on output prediction errors. For control problems requiring asymptotic tracking of a reference input we provide sufficient conditions under which the switched closed-loop control system is exponentially stable and asymptotically achieves good control even if the switching does not stop, Our results are illustrated with three examples     

Robust backstepping control for a class of time delayed systems

In this note, the problem of robust output feedback control for a class of nonlinear time delayed systems is considered. The systems considered are in strict-feedback form. State observer is first designed, then based on the observed states the controller is designed via backstepping method. Both the designed observer and controller are independent of the time delays. Based on Lyapunov stability theory, we prove that the constructed controller can render the closed-loop system asymptotically stable. Simulation results further verify the effectiveness of the proposed approach.     

同时镇定一族带有不确定参数的多输入非线性系统

Simultaneous stabilization for a collection of multi-input nonlinear systems with uncertain parameters is dealt with in this paper. A systematic method for obtaining a control Lyapunov function (CLF) is presented by solving the Lyapunov equation. A sufficient condition that a quadratic CLF is a common CLF for these systems is acquired. A continuous state feedback is designed to simultaneously stabilize these systems. Finally, the effectiveness of the proposed scheme is illustrated by a simulation example.     

Disturbance-observer-based robust control for time delay uncertain systems

A robust control scheme is proposed for a class of systems with uncertainty and time delay based on disturbance observer technique. A disturbance observer is developed to estimate the disturbance generated by an exogenous system, and the design parameters of the disturbance observer are determined by solving linear matrix inequalities (LMIs). Based on the output of the disturbance observer, a robust control scheme is proposed for the time delay uncertain system. The disturbance-observer-based robust controller is combined of two parts: one is a linear feedback controller designed using LMIs and the other is a compensatory controller designed with the output of the disturbance observer. By choosing an appropriate Lyapunov function candidate, the stability of the closed-loop system is proved. Finally, simulation example is presented to illustrate the effectiveness of the proposed control scheme.     

不确定广义双线性系统的鲁棒镇定

针对带有不确定参数的广义双线性系统的鲁棒镇定问题进行研究, 其中不确定参数是时变且范数有界的. 本文的目的是设计状态反馈控制器, 使得对所有满足条件的不确定参数闭环系统都是渐近稳定的. 通过引入广义二次稳定的概念、采用Lyapunov方法, 分别给出了不确定广义双线性系统在两种不同情形下可镇定的充分条件; 此外, 两个数值例子分别说明了两种设计方法的有效性和合理性.     

Output feedback fault-tolerant control for a class of discrete-time fuzzy bilinear systems

This paper studies the fault-tolerant control problem for a class of discrete-time fuzzy bilinear systems with unmeasurable states. A fuzzy detective observer is designed to detect the faults. Based on the fuzzy detective observer, a fuzzy controller is designed by solving a set of linear matrix inequalities (LMIs) to ensure that the closed-loop system without faults is asymptotically stable. For the discrete-time fuzzy bilinear system with faults, a fuzzy adaptive diagnostic observer is designed to estimate the faults by solving a set of LMIs. Then, a fuzzy faulttolerant controller is designed based on the fuzzy diagnostic observer to ensure that the closed-loop system with faults is asymptotically stable. At last, simulation results are presented to verify the effectiveness of the proposed output feedback fault-tolerant control method.     

多故障网络控制系统模态依赖下的H_∞控制

针对存在传感器失效、随机丢包和时延等多故障的网络控制系统,建立了系统的转换模态。通过运用Lyapunov和LMI判定方法,研究了系统在模态依赖下渐近稳定的充分条件。设计了传感器失效的模型,提出了控制器的设计方法,运用鲁棒H∞控制方法,改善了闭环网络控制系统的性能。通过仿真实例验证了该方法的可行性和有效性。     

具有数据丢包的非线性奇异脉冲系统量化控制

考虑网络传输中存在的数据丢包和信号量化问题, 研究了基于数据丢包的非线性奇异脉冲系统设量化反馈控制器的设计方法. 首先给出一般非线性奇异脉冲系统的数学描述, 并在此基础上建立相应的具有丢包的闭环量化反馈控制系统的数学模型. 其次, 根据李雅普诺夫稳定性理论, 给出了奇异脉冲系统的渐近稳定的充分条件以及量化反馈控制器的设计方法. 应用本设计方法, 可以选择满足代数矩阵不等式条件的量化反馈增益, 实现系统渐近稳定. 最后通过对Chua混沌系统仿真, 表明利用本文设计的量化控制器能够保证闭环非线性奇异脉冲系统在具有数据丢包的情况下渐近稳定.     

Controller design for stochastic Markovian switching systems with time-varying delay and actuator saturation

The paper deals with controller design for stochastic Markovian switching systems with time-varying delay and actuator saturation by implying a new criterion for the domain of attraction firstly. By constructing more appropriate Lyapunov–Krasovskii functional, some new conditions for verifying stochastic stability of the plant are established. Then, the state feedback controller is designed to expand the domain of attraction of the corresponding closed-loop system. The procedure of deriving controller gain matrices is converted into an optimisation problem with constraints of a set of linear matrix inequalities. The mathematical model of RLC series circuit illustrates the validity of the obtained results.     

Adaptive output feedback control of feedforward nonlinear distributed delay systems with unknown delay kernel

This paper considers the problem of global adaptive output feedback regulation for a class of uncertain feedforward nonlinear distributed delay systems. Compared with the existing results, we reduce the conservatism of the restrictive conditions by combining the dynamic scaling technique and the backstepping method, in particular, uncertain control coefficients and unknown delay kernels are admitted. With the help of the Lyapunov–Krasovskii theorem, a delay-independent output feedback controller is proposed by constructing an input-driven observer with a novel dynamic gain, which guarantees that all the closed-loop signals are globally bounded while rendering the states of original system and the estimate states globally asymptotically to converge to zero as time goes to infinity. Finally, a numerical example is given to illustrate the usefulness of our results.