具有执行器/控制器故障的时滞系统稳定性与反馈控制
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摘要
在工业生产过程中,时滞现象普遍存在.不仅如此,控制系统在运行过程中,内部元件如控制器、执行器发生失效不可避免,这些都将导致系统性能下降甚至不稳,同时使得控制系统的分析和综合变得更加复杂,给控制系统的研究带来了新的挑战.
不同于原有的可靠控制设计方案,本文引进了切换策略,利用切换系统的理论框架研究了具有执行器或控制器故障的时滞系统的稳定性及反馈控制问题.因连续动态、离散动态与时滞的相互作用和影响,使得这类系统的动态行为变得十分复杂,系统的运行机制远未清楚,大量问题亟待解决.本文通过构造分段Lyapunov-Krasovskii泛函,基于平均驻留时间技术、多Lyapunov函数的方法,采用积分不等式、自由加权矩阵、广义系统模型变换并结合Moon不等式等方法,研究因执行器或控制器故障导致的切换时滞系统的稳定性及控制器设计的一些问题,主要工作包括:
针对多时变时滞不确定系统的状态反馈控制器彻底失效情况,通过将系统模型转化为包含稳定子系统和不稳定子系统的切换时滞系统模型,将切换时滞系统的激活时间划分为稳定子系统的激活时间和不稳定子系统的激活时间,采用平均驻留时间的方法并结合积分不等式,构造分段Lyapunov-Krasovskii泛函,证明了当切换时滞系统的平均驻留时间以及稳定子系统与不稳定子系统的激活时间之比不小于某一常数时,所设计的切换机制可以保证切换时滞系统是鲁棒指数稳定.本文还进一步推广到含有非线性扰动的情形.
针对单时变时滞不确定系统的状态反馈控制器彻底失效情况,分别讨论了具有非线性干扰的不确定时滞系统、不确定区间时变时滞系统的状态反馈控制器的可解问题.首先针对具有非线性干扰的不确定时滞系统,利用所建立的鲁棒指数稳定的充分条件,通过采用矩阵变换,引进新的矩阵变量,获得了控制器可解的充分条件.类似地,针对不确定区间时变时滞系统,利用Lyapunov-Krasovskii泛函,结合积分不等式,得到了具有区间时变时滞的鲁棒指数稳定充分条件,进而给出控制器具体设计方案.最后通过数值例子验证了所提出方法的有效性.
针对时变时滞不确定系统的执行器部分失效情况,分别讨论了包含稳定子系统和不稳定子系统的切换时滞系统的稳定性问题以及子系统均稳定的切换时滞系统的输出反馈控制器的设计问题.首先针对稳定与不稳定子系统共存的切换时滞系统,利用平均驻留时间技术及稳定与不稳定子系统的激活时间之比,给出时滞系统在某一合适时滞上界是鲁棒指数稳定的充分条件.特别地,通过求解LMIs,得到了保证时滞系统指数稳定所允许的时滞上界.针对子系统均稳定的切换时滞系统,利用广义系统模型变换并结合Moon不等式方法,通过锥补线性化算法,给出了确保所考虑系统鲁棒指数稳定的混杂动态输出反馈控制器设计方案.
针对区间时变时滞线性系统的执行器部分失效情况,通过将系统模型转化为区间时变时滞切换系统,基于平均驻留时间技术,采用自由加权矩阵方法,得到时滞相关且依赖时滞区间的指数稳定及镇定的充分条件,从而解决了具有执行器失效故障的区间时变时滞系统指数稳定的混杂状态反馈控制器的设计问题.由于充分考虑了时滞下界的信息,所得结果具有更小的保守性.仿真例子表明所提出的方法确实有效.
针对区间时变时滞不确定中立时滞系统的执行器部分失效情况,通过将系统模型转化为区间时变时滞不确定切换中立时滞系统,利用平均驻留时间技术及结合积分不等式,设计混杂状态反馈控制器并以LMIs形式给出闭环系统鲁棒指数稳定的充分条件.特别地,又得到了切换时滞系统的鲁棒指数镇定充分条件.
针对执行器卡死故障,研究基于观测器的不确定时滞系统自适应控制问题.将系统模型转化成切换时滞系统,利用多Lyapunov函数方法,基于分段Lyapunov稳定性理论,设计了自适应控制器使得闭环系统渐近稳定并给出了系统渐近稳定的时滞无关充分条件.
Time delay phnomenon widely exists in many industrial processes. Also, the faults of components such as actuators, controllers, occur inevitably with the running of systems. These may result in instability and poor performance of the resulting systems and complicate stability analysis and synthesis of the control systems. Therefore, it is a challenge for us to study this class of systems.
Different from the design of the original reliable control, the paper mainly focuses on stability and feedback control of time-delay systems with actuator/controller failures by introducing a switching strategy and utilizing the framwork of switched system. Due to the interaction among the continuous dynamics, discrete dynamics and time delays, the behavior of such systems is very complicated. Mechanism of system evolution is not clear and many problems of analysis and syntheses need to be studied. Here, some problems of stability and controller design of the resulting closed-loop systems caused by actuator/controllelr failures are considered by constructing the piecewise Lyapunov-Krasovskii functional and by applying methods such as the average dwell time technique, multiple Lyapunov function method, the integral inequality, free weighting matrices, a combination of descriptor model transformation approach and Moon's integral inequality and so on. The main contributions of this dissertation are as follows.
The issue of robustly exponential stability for a class of multi-delay systems with structure uncertainties or/and nonlinear perturbations and controller failures, is considered. Multi-delay system with actuator failures is modelled as a special switched delay system including both stable and unstable subsystems. Based on the average dwell time concept and using the integral inequality and the piecewise Lyapunov-Krasovskii functional, it is proved theoretically that the given switched system is robustly exponentially stable with a desired stability margin by dividing the total activation time into the time with stable subsystems and the time with unstable subsystems, in the context that the average dwell time and the ratio of the activation time with stable subsystems to the activation time with unstable subsystems are not less than a specified constant. And the resullts are extended to the case with nonlinear perturbations.
The sovable problem of state feedback controller for the delay systems with both structure uncertainties and nonlinear perturbations is considered. Utilizing the established robustly exponentially sufficient condition and using matrix transformation, the sovable condition is obtained by introducing new matrix varables. Similarly, by using Lyapunov-Krasovskii functional, the delay-range-dependent stability condition is given in terms of LMIs and the sovable condition of the uncertain system with interval time-varying delay is also obtained.
The stability property for uncertain switched delay systems caused by actuator failures, which are composed of stable subsystems and unstable ones, is addressed. By using the average dwell time idea and the total activation time ratio between stable subsystems and unstable ones, it is shown theoretically that the resulting closed-loop system is robustly exponentially stable for an allowable upper bound of delays if its corresponding system with zero delay is exponentially stable. Particularly, the maximal allowable upper bound of delays can be obtained by solving some feasible linear matrix inequalities. Then, the design problem of hybrid dynamical output feedback controller for robustly exponential stabilization of a class of uncertain systems with time-varying delays and controller failures is investigated. By representing the time-delay system in the descriptor form and using the average dwell time technique, a new delay-dependent stabilization criterion for the existence of output feedback controllers is obtained in terms of matrix inequalities. A cone complementary linearization algorithm is utilized such that the resulting closed-loop switched systems are stable for the normal and/or faulty cases.
The issue of exponential stabilization for a class of special time-varying delay switched systems resulting from actuator faults is considered. The time-varying delay is assumed to belong to an interval and can be slow or fast time-varying function. Based on the average dwell time method incorporating with free weighting matrices, a hybrid state feedback strategy is redesigned to guarantee the stability of the system. New delay-range-dependent stabilization conditions using state feedback controllers are formulated in terms of linear matrix inequalities by choosing appropriate Lyapunov-Krasovskii functional without neglecting some useful knowledge on system states. The obtained results are less conserva tive. Numerical examples are given to demonstrate the feasiblity and the effectiveness of the proposed method.
The problems of delay-dependent robustly exponential stability and stabilization of a class of special neutral systems with interval time-varying delays and actuator failures, are investigated. For the special switched neutral system resulting from actuator failures, based on the switching strategy of average dwell time method and the integral inequality approach, the delay-dependent sufficient conditions for exponential stability and stabilization of the special switched neutral systems are established in terms of linear matrix inequalities by choosing appropriate piecewise Lyapunov-Krasovskii functional. Also, the stabilizing hybrid state-feedback controllers are designed to guarantee that the closed-loop system is robustly exponentially stable. Particularly, the stabilization of the switched delay systems are obtained.
This paper concerns the observer-based adaptive control problem of uncertain time-delay systems with stuck actuator faults. The system model is expressed as a switched system. Under the case that the original controller cannot stabilize the faulty system, multiple adaptive controllers are designed and suitable switching logic is incorporated to ensure the closed-loop system stable and state tracking. New delay-independent sufficient conditions for asymptotic stability are obtained based on piecewise Lyapunov stability theory.
不同于原有的可靠控制设计方案,本文引进了切换策略,利用切换系统的理论框架研究了具有执行器或控制器故障的时滞系统的稳定性及反馈控制问题.因连续动态、离散动态与时滞的相互作用和影响,使得这类系统的动态行为变得十分复杂,系统的运行机制远未清楚,大量问题亟待解决.本文通过构造分段Lyapunov-Krasovskii泛函,基于平均驻留时间技术、多Lyapunov函数的方法,采用积分不等式、自由加权矩阵、广义系统模型变换并结合Moon不等式等方法,研究因执行器或控制器故障导致的切换时滞系统的稳定性及控制器设计的一些问题,主要工作包括:
针对多时变时滞不确定系统的状态反馈控制器彻底失效情况,通过将系统模型转化为包含稳定子系统和不稳定子系统的切换时滞系统模型,将切换时滞系统的激活时间划分为稳定子系统的激活时间和不稳定子系统的激活时间,采用平均驻留时间的方法并结合积分不等式,构造分段Lyapunov-Krasovskii泛函,证明了当切换时滞系统的平均驻留时间以及稳定子系统与不稳定子系统的激活时间之比不小于某一常数时,所设计的切换机制可以保证切换时滞系统是鲁棒指数稳定.本文还进一步推广到含有非线性扰动的情形.
针对单时变时滞不确定系统的状态反馈控制器彻底失效情况,分别讨论了具有非线性干扰的不确定时滞系统、不确定区间时变时滞系统的状态反馈控制器的可解问题.首先针对具有非线性干扰的不确定时滞系统,利用所建立的鲁棒指数稳定的充分条件,通过采用矩阵变换,引进新的矩阵变量,获得了控制器可解的充分条件.类似地,针对不确定区间时变时滞系统,利用Lyapunov-Krasovskii泛函,结合积分不等式,得到了具有区间时变时滞的鲁棒指数稳定充分条件,进而给出控制器具体设计方案.最后通过数值例子验证了所提出方法的有效性.
针对时变时滞不确定系统的执行器部分失效情况,分别讨论了包含稳定子系统和不稳定子系统的切换时滞系统的稳定性问题以及子系统均稳定的切换时滞系统的输出反馈控制器的设计问题.首先针对稳定与不稳定子系统共存的切换时滞系统,利用平均驻留时间技术及稳定与不稳定子系统的激活时间之比,给出时滞系统在某一合适时滞上界是鲁棒指数稳定的充分条件.特别地,通过求解LMIs,得到了保证时滞系统指数稳定所允许的时滞上界.针对子系统均稳定的切换时滞系统,利用广义系统模型变换并结合Moon不等式方法,通过锥补线性化算法,给出了确保所考虑系统鲁棒指数稳定的混杂动态输出反馈控制器设计方案.
针对区间时变时滞线性系统的执行器部分失效情况,通过将系统模型转化为区间时变时滞切换系统,基于平均驻留时间技术,采用自由加权矩阵方法,得到时滞相关且依赖时滞区间的指数稳定及镇定的充分条件,从而解决了具有执行器失效故障的区间时变时滞系统指数稳定的混杂状态反馈控制器的设计问题.由于充分考虑了时滞下界的信息,所得结果具有更小的保守性.仿真例子表明所提出的方法确实有效.
针对区间时变时滞不确定中立时滞系统的执行器部分失效情况,通过将系统模型转化为区间时变时滞不确定切换中立时滞系统,利用平均驻留时间技术及结合积分不等式,设计混杂状态反馈控制器并以LMIs形式给出闭环系统鲁棒指数稳定的充分条件.特别地,又得到了切换时滞系统的鲁棒指数镇定充分条件.
针对执行器卡死故障,研究基于观测器的不确定时滞系统自适应控制问题.将系统模型转化成切换时滞系统,利用多Lyapunov函数方法,基于分段Lyapunov稳定性理论,设计了自适应控制器使得闭环系统渐近稳定并给出了系统渐近稳定的时滞无关充分条件.
Time delay phnomenon widely exists in many industrial processes. Also, the faults of components such as actuators, controllers, occur inevitably with the running of systems. These may result in instability and poor performance of the resulting systems and complicate stability analysis and synthesis of the control systems. Therefore, it is a challenge for us to study this class of systems.
Different from the design of the original reliable control, the paper mainly focuses on stability and feedback control of time-delay systems with actuator/controller failures by introducing a switching strategy and utilizing the framwork of switched system. Due to the interaction among the continuous dynamics, discrete dynamics and time delays, the behavior of such systems is very complicated. Mechanism of system evolution is not clear and many problems of analysis and syntheses need to be studied. Here, some problems of stability and controller design of the resulting closed-loop systems caused by actuator/controllelr failures are considered by constructing the piecewise Lyapunov-Krasovskii functional and by applying methods such as the average dwell time technique, multiple Lyapunov function method, the integral inequality, free weighting matrices, a combination of descriptor model transformation approach and Moon's integral inequality and so on. The main contributions of this dissertation are as follows.
The issue of robustly exponential stability for a class of multi-delay systems with structure uncertainties or/and nonlinear perturbations and controller failures, is considered. Multi-delay system with actuator failures is modelled as a special switched delay system including both stable and unstable subsystems. Based on the average dwell time concept and using the integral inequality and the piecewise Lyapunov-Krasovskii functional, it is proved theoretically that the given switched system is robustly exponentially stable with a desired stability margin by dividing the total activation time into the time with stable subsystems and the time with unstable subsystems, in the context that the average dwell time and the ratio of the activation time with stable subsystems to the activation time with unstable subsystems are not less than a specified constant. And the resullts are extended to the case with nonlinear perturbations.
The sovable problem of state feedback controller for the delay systems with both structure uncertainties and nonlinear perturbations is considered. Utilizing the established robustly exponentially sufficient condition and using matrix transformation, the sovable condition is obtained by introducing new matrix varables. Similarly, by using Lyapunov-Krasovskii functional, the delay-range-dependent stability condition is given in terms of LMIs and the sovable condition of the uncertain system with interval time-varying delay is also obtained.
The stability property for uncertain switched delay systems caused by actuator failures, which are composed of stable subsystems and unstable ones, is addressed. By using the average dwell time idea and the total activation time ratio between stable subsystems and unstable ones, it is shown theoretically that the resulting closed-loop system is robustly exponentially stable for an allowable upper bound of delays if its corresponding system with zero delay is exponentially stable. Particularly, the maximal allowable upper bound of delays can be obtained by solving some feasible linear matrix inequalities. Then, the design problem of hybrid dynamical output feedback controller for robustly exponential stabilization of a class of uncertain systems with time-varying delays and controller failures is investigated. By representing the time-delay system in the descriptor form and using the average dwell time technique, a new delay-dependent stabilization criterion for the existence of output feedback controllers is obtained in terms of matrix inequalities. A cone complementary linearization algorithm is utilized such that the resulting closed-loop switched systems are stable for the normal and/or faulty cases.
The issue of exponential stabilization for a class of special time-varying delay switched systems resulting from actuator faults is considered. The time-varying delay is assumed to belong to an interval and can be slow or fast time-varying function. Based on the average dwell time method incorporating with free weighting matrices, a hybrid state feedback strategy is redesigned to guarantee the stability of the system. New delay-range-dependent stabilization conditions using state feedback controllers are formulated in terms of linear matrix inequalities by choosing appropriate Lyapunov-Krasovskii functional without neglecting some useful knowledge on system states. The obtained results are less conserva tive. Numerical examples are given to demonstrate the feasiblity and the effectiveness of the proposed method.
The problems of delay-dependent robustly exponential stability and stabilization of a class of special neutral systems with interval time-varying delays and actuator failures, are investigated. For the special switched neutral system resulting from actuator failures, based on the switching strategy of average dwell time method and the integral inequality approach, the delay-dependent sufficient conditions for exponential stability and stabilization of the special switched neutral systems are established in terms of linear matrix inequalities by choosing appropriate piecewise Lyapunov-Krasovskii functional. Also, the stabilizing hybrid state-feedback controllers are designed to guarantee that the closed-loop system is robustly exponentially stable. Particularly, the stabilization of the switched delay systems are obtained.
This paper concerns the observer-based adaptive control problem of uncertain time-delay systems with stuck actuator faults. The system model is expressed as a switched system. Under the case that the original controller cannot stabilize the faulty system, multiple adaptive controllers are designed and suitable switching logic is incorporated to ensure the closed-loop system stable and state tracking. New delay-independent sufficient conditions for asymptotic stability are obtained based on piecewise Lyapunov stability theory.
引文
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