广义系统与广义随机系统的容错控制
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摘要
广义系统是一类更具广泛形式的动力学系统,描述了一类更为广泛的实际系统模型,例如电力系统、经济系统、机器人系统、电子网络系统和宇航系统等,对它的研究具有重要的理论意义和应用价值。广义系统历经三十多年的研究,关于广义系统稳定性、能控性以及能观性等方面的理论已有相当成熟的结果,但是对容错控制问题的研究不够深入,它是在广义控制系统发展的逐步完善基础上发展起来的,因此,对广义系统的容错控制研究有着广阔的发展前途,其理论还有待进一步发展和完善。本文结合广义系统的理论成果与正常系统容错控制的思想,研究了广义系统与广义随机系统的容错控制问题。
由于实际工程中,除了对系统的Lyapunov稳定性感兴趣外,更关心系统能满足一定的暂态性能要求,即有限时间控制问题。本文研究基于观测器的广义系统有限时间稳定问题,利用广义状态观测器理论,设计基于观测器的状态反馈控制器,使闭环系统无脉冲模和有限时间稳定;同时也研究了不确定广义系统的有限时间容错控制问题,基于线性矩阵不等式(LMI),给出了执行器故障情形下,系统具有完整性的鲁棒有限时间容错控制设计方法。
利用LMI方法,研究了更具一般性的连续故障模型的容错保性能控制和鲁棒H∞容错控制问题。针对一类不确定广义系统,结合一个二次性能函数,研究广义系统执行器发生故障时,故障闭环系统保持正则、稳定、无脉冲,且闭环性能指标不超过某个确定界的状态反馈可靠保性能控制律的设计问题;讨论了具有状态时滞和参数不确定性的广义系统的鲁棒H∞容错控制问题,基于广义Riccati不等式,给出了执行器故障时闭环系统仍保持稳定的充分条件和控制器的设计方法。
由于处理非线性系统时,对Hamilton-Jacobi-Inequality(HJI)的求解很困难,无论是解析解还是数值解。本文利用Takagi-Sugeno (T-S)模糊模型来模拟或逼近非线性系统,将执行器故障按故障范围进行分类,构造故障切换系统,设计状态反馈切换控制器,使切换系统对任意切换律是H∞渐近稳定的。另外研究了广义非线性系统的可靠H∞输出跟踪控制问题,设计模糊可靠控制器,使系统在执行器故障时仍能跟踪参考信号,且跟踪误差系统渐近稳定并满足给定的H∞跟踪性能指标。
基于随机微分方程的稳定性理论,本文研究了广义随机系统的稳定性与可靠控制问题。针对Markov跳跃非线性广义系统的鲁棒随机镇定和H∞控制问题,将具有范数有界不确定性和Markov跳跃参数的广义非线性系统用T-S模糊模型描述,利用随机Lyapunov函数,设计状态反馈模糊控制器,使闭环模糊系统鲁棒随机稳定,且H∞范数有界。对不确定广义随机模糊系统的鲁棒H∞可靠控制问题,利用LMI方法,给出了鲁棒H∞可靠模糊控制器存在的充分条件和设计方法;同时还研究了非线性广义随机时滞系统的鲁棒可靠保性能控制问题,设计状态反馈模糊控制器,使闭环系统对不确定性和执行器故障是随机稳定的,且给定的性能指标不超过某个上界。
Singular systems is a kind of dynamics systems, which is more general and more natural to represent and to handle practical model such as power systems, economic systems, robotic systems, electrical network systems, astronavigation systems, and so on. The research on singular systems is of important theoretical meaning and practical significance. In the last three decades, there have been a lot of achievements on the stability, controllability, observerability etc, but few efforts were paid to fault tolerant control for singular systems. So there is great space for the development of fault tolerant control for singular systems. In the light of theoretical results of singular systems and that of fault tolerant control for normal systems, we provide a study on the theory of fault tolerant control for singular systems and singular stochastic systems.
In practical engineering, except for Lyapunov stability, we paid more attention to the behavior of the systems over a fixed finite time interval, which is called finite- time control problems. An observer-based finite-time control problem for linear singular systems is considered. By using generalized state-observer theory, we design the observer-based state feedback controller, which guarantees that the resultant closed-loop system is impulse free and finite-time stable. Moreover, this paper deals with the finite-time fault-tolerant control problem for uncertain singular system, whose class is with parameter uncertainties and norm bounded. Based on LMI, the integrity design technique with actuators failures is analyzed based on robust fault-tolerant control theory.
Based on LMI method, reliable guaranteed cost control and robust H∞fault tolerant control problems are studied, which is a more general actuator failure model. For a class of linear descriptor systems with uncertainty and a given quadratic cost function, we design a reliable guaranteed cost state feedback control law such that, the closed-loop descriptor systems keep regular, impulse-free and stable in the case of actuator failures. Meanwhile, a certain upper bound of a quadratic cost index can be guaranteed. Robust H∞fault-tolerant control of a kind of descriptor delay linear systems with uncertainty and disturbance is studied. In the circumstance of actuator failures, on the basis of generalized Riccati inequality, we obtain the sufficient condition for the systems possessing asymptotical stability against actuator failures and the design method of the controller.
It is well known that the Hamliton-Jacobi inequality (HJI) is difficult to resolve, either analytically or numerically. So, the nonlinear system is represented or approximated by a T-S fuzzy model. Actuator failures are classified in terms of extent of failures. Faulty switching system is constructed respect to various classes of actuator failures. A state-feedback-switching controller is designed such that the closed-loop switched system is asymptotically stable with a prescribed H∞performance constraint for arbitrary switching law. Furthermore, we investigate the problem of reliable H∞output tracking control for a class of nonlinear singular system using Takagi-Sugeno (T-S) fuzzy model approach. When the actuator failures cases occurred, a reliable controller is deigned such that the system output follows that of a reference model while satisfying a prescribed H∞performance constraint.
The stability and reliable control problems are studied in terms of stability theory for stochastic differential equations. We deal with the problems of robust stochastic stabilization and robust H∞control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The T-S fuzzy model is employed to represent a nonlinear singular system with norm-bounded parameter uncertainties and Markovian jump parameters. Based on stochastic Lyapunov function method, a state feedback fuzzy controller is designed such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties, and a prescribed performance is achieved. At the same time, we deal with the design problem of robust H∞reliable control for nonlinear singular stochastic systems with actuator failures. Based on LMI techniques, we establish sufficient conditions of existence and design method of robust H∞reliable fuzzy controller. Finally, the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems is studied. A state feedback fuzzy controller is designed such that the resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties as well as different actuator fault cases.
由于实际工程中,除了对系统的Lyapunov稳定性感兴趣外,更关心系统能满足一定的暂态性能要求,即有限时间控制问题。本文研究基于观测器的广义系统有限时间稳定问题,利用广义状态观测器理论,设计基于观测器的状态反馈控制器,使闭环系统无脉冲模和有限时间稳定;同时也研究了不确定广义系统的有限时间容错控制问题,基于线性矩阵不等式(LMI),给出了执行器故障情形下,系统具有完整性的鲁棒有限时间容错控制设计方法。
利用LMI方法,研究了更具一般性的连续故障模型的容错保性能控制和鲁棒H∞容错控制问题。针对一类不确定广义系统,结合一个二次性能函数,研究广义系统执行器发生故障时,故障闭环系统保持正则、稳定、无脉冲,且闭环性能指标不超过某个确定界的状态反馈可靠保性能控制律的设计问题;讨论了具有状态时滞和参数不确定性的广义系统的鲁棒H∞容错控制问题,基于广义Riccati不等式,给出了执行器故障时闭环系统仍保持稳定的充分条件和控制器的设计方法。
由于处理非线性系统时,对Hamilton-Jacobi-Inequality(HJI)的求解很困难,无论是解析解还是数值解。本文利用Takagi-Sugeno (T-S)模糊模型来模拟或逼近非线性系统,将执行器故障按故障范围进行分类,构造故障切换系统,设计状态反馈切换控制器,使切换系统对任意切换律是H∞渐近稳定的。另外研究了广义非线性系统的可靠H∞输出跟踪控制问题,设计模糊可靠控制器,使系统在执行器故障时仍能跟踪参考信号,且跟踪误差系统渐近稳定并满足给定的H∞跟踪性能指标。
基于随机微分方程的稳定性理论,本文研究了广义随机系统的稳定性与可靠控制问题。针对Markov跳跃非线性广义系统的鲁棒随机镇定和H∞控制问题,将具有范数有界不确定性和Markov跳跃参数的广义非线性系统用T-S模糊模型描述,利用随机Lyapunov函数,设计状态反馈模糊控制器,使闭环模糊系统鲁棒随机稳定,且H∞范数有界。对不确定广义随机模糊系统的鲁棒H∞可靠控制问题,利用LMI方法,给出了鲁棒H∞可靠模糊控制器存在的充分条件和设计方法;同时还研究了非线性广义随机时滞系统的鲁棒可靠保性能控制问题,设计状态反馈模糊控制器,使闭环系统对不确定性和执行器故障是随机稳定的,且给定的性能指标不超过某个上界。
Singular systems is a kind of dynamics systems, which is more general and more natural to represent and to handle practical model such as power systems, economic systems, robotic systems, electrical network systems, astronavigation systems, and so on. The research on singular systems is of important theoretical meaning and practical significance. In the last three decades, there have been a lot of achievements on the stability, controllability, observerability etc, but few efforts were paid to fault tolerant control for singular systems. So there is great space for the development of fault tolerant control for singular systems. In the light of theoretical results of singular systems and that of fault tolerant control for normal systems, we provide a study on the theory of fault tolerant control for singular systems and singular stochastic systems.
In practical engineering, except for Lyapunov stability, we paid more attention to the behavior of the systems over a fixed finite time interval, which is called finite- time control problems. An observer-based finite-time control problem for linear singular systems is considered. By using generalized state-observer theory, we design the observer-based state feedback controller, which guarantees that the resultant closed-loop system is impulse free and finite-time stable. Moreover, this paper deals with the finite-time fault-tolerant control problem for uncertain singular system, whose class is with parameter uncertainties and norm bounded. Based on LMI, the integrity design technique with actuators failures is analyzed based on robust fault-tolerant control theory.
Based on LMI method, reliable guaranteed cost control and robust H∞fault tolerant control problems are studied, which is a more general actuator failure model. For a class of linear descriptor systems with uncertainty and a given quadratic cost function, we design a reliable guaranteed cost state feedback control law such that, the closed-loop descriptor systems keep regular, impulse-free and stable in the case of actuator failures. Meanwhile, a certain upper bound of a quadratic cost index can be guaranteed. Robust H∞fault-tolerant control of a kind of descriptor delay linear systems with uncertainty and disturbance is studied. In the circumstance of actuator failures, on the basis of generalized Riccati inequality, we obtain the sufficient condition for the systems possessing asymptotical stability against actuator failures and the design method of the controller.
It is well known that the Hamliton-Jacobi inequality (HJI) is difficult to resolve, either analytically or numerically. So, the nonlinear system is represented or approximated by a T-S fuzzy model. Actuator failures are classified in terms of extent of failures. Faulty switching system is constructed respect to various classes of actuator failures. A state-feedback-switching controller is designed such that the closed-loop switched system is asymptotically stable with a prescribed H∞performance constraint for arbitrary switching law. Furthermore, we investigate the problem of reliable H∞output tracking control for a class of nonlinear singular system using Takagi-Sugeno (T-S) fuzzy model approach. When the actuator failures cases occurred, a reliable controller is deigned such that the system output follows that of a reference model while satisfying a prescribed H∞performance constraint.
The stability and reliable control problems are studied in terms of stability theory for stochastic differential equations. We deal with the problems of robust stochastic stabilization and robust H∞control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The T-S fuzzy model is employed to represent a nonlinear singular system with norm-bounded parameter uncertainties and Markovian jump parameters. Based on stochastic Lyapunov function method, a state feedback fuzzy controller is designed such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties, and a prescribed performance is achieved. At the same time, we deal with the design problem of robust H∞reliable control for nonlinear singular stochastic systems with actuator failures. Based on LMI techniques, we establish sufficient conditions of existence and design method of robust H∞reliable fuzzy controller. Finally, the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems is studied. A state feedback fuzzy controller is designed such that the resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties as well as different actuator fault cases.
引文
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