多指标约束的动态系统容错控制
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摘要
容错控制是为了提高系统的可靠性、安全性而提出的一种新的控制策略,其理论意义在于当动态系统发生故障时仍然可以稳定运行,并具有可以接受的动、静态性能。目前,针对多指标约束条件下的容错控制研究还处于起步阶段,所得到的一些成果还局限在线性连续系统。基于以上的考虑,本文主要以广义系统、区间系统和非线性系统为研究对象,兼顾控制器的不确定性,考虑其在多指标约束条件下的容错控制问题,提出了以上系统的多指标约束条件下的满意容错控制方法,推导和论证了非脆弱满意容错控制器的设计方法和存在条件,以期建立更完善的满意容错控制理论和多指标约束容错控制方法,为其能更好地应用于工程实际做好理论铺垫,所取得的主要研究成果与创新点如下:
(1)提出了不确定广义系统和不确定时滞广义系统在区域极点指标、H_∞指标、方差上界指标及保成本指标约束条件下的满意容错控制器设计方法及滤波器设计方法。在执行器故障条件下,利用线性矩阵不等式(LMI,Linear matrix inequality)分析了相容指标的取值范围和多指标约束下容错控制器存在的充分条件,并给出控制器的设计方法。
(2)针对不确定线性系统和线性系统族,提出了非脆弱容错控制设计方法。在考虑控制器不确定性的情况下,给出了一种综合区域极点约束、最小方差上界约束和H_∞约束的非脆弱容错控制设计方法,并分析了三种指标的相容性;同时又提出了一种主动容错控制设计方法。通过神经网络对故障进行辨识、定位和诊断,结合多模型参考方法,给出了一种主动容错控制设计方法。
(3)针对无时滞和带有时滞的两类区间系统,给出了各自的容错控制器设计方法。将带有执行器故障的不确定系统转化为区间系统,应用区间系统的相关理论解决了不确定系统的容错控制问题。应用LMI把相关性能指标约束对应的不等式问题转化为凸优化问题,最后通过解线性矩阵不等式,得到满足性能指标要求的控制器。
(4)提出了两类T-S模糊系统的多指标约束容错控制设计方法。一类是T-S模糊状态时滞系统,并综合考虑全局模糊模型的不确定性和执行器故障,提出了一种模糊H_∞保成本容错控制的思想,并利用LMI把相应的模糊控制问题转化成凸优化问题,给出了模糊H_∞保成本容错控制器的表达式。另一类是针对T-S模糊广义系统,在保证其二次稳定的前提条件下,兼顾系统的H_2和H_∞性能混合指标约束下的容错控制器设计问题,保证了整个闭环模糊非线性广义系统的二次稳定性和良好的动态品质和稳态性能。
(5)针对不确定部分具有范数有界约束,非线性部分满足线性有界约束的不确定非线性系统,提出了一种多指标约束条件下的容错控制器设计方法。利用LMI结合Lyapunov稳定性理论研究了一种复杂的不确定非线性时滞系统的H_∞保成本容错控制问题。综合考虑了当系统的执行器发生故障和控制器参数发生摄动时,系统的非脆弱H_∞保成本控制问题,给出了非脆弱H_∞保成本容错控制律的存在条件和设计方法;同时应用有记忆状态反馈控制器,提出了多时滞混沌系统的H_∞混沌同步控制设计方法,对于模型结构发生变化,输入改变的情况,又给出了一种非线性容错控制器的设计方法。
最后,指出了本文中还存在的问题和需要进一步探讨的研究方向。
Fault tolerant control is a novel strategy to improve the security and reliability of systems. Its meaning is that dynamical systems can run safely under the acceptable dynamical and stable performances when the faults of dynamic systems occur. Now, the study on fault tolerant control under multi-index constraints is still in primary stage, the results are mainly for normal linear systems. Based on the above consideration, this dissertation consider singular systems, interval systems and non-linear systems, study the fault tolerant control problems for them under the constraints of multiple indexes, propose the satisfactory fault tolerant control for them , deduce the existing conditions and design method of non-fragile satisfactory fault tolerant controller, so as to improve the fault tolerant control theory under multi-index constraints, thus provide a theoretical backbone for its engineering applications. The principal research results and innovations are outlined as follows:
(1) The design methods of satisfactory fault tolerant controllers and filters of uncertain singular systems, along with its time-delayed versions, are proposed, comprehensively considering regional pole index, H_∞constraint, variance upper bound and cost guaranteed constraint. We adopt the fault model of actuator, analyze the value ranges of compatible indexes and sufficient conditions for the existing of fault tolerant controller under the constraint of multiple indexes, and a constructive design method of controller is given.
(2) The problem of non-fragile fault tolerant control of uncertain linear system and linear system famlies are proposed, with the consideration of uncertainty of controllers. The regional pole index, minimal variance upper bound index and H_∞index are considered comprehensively. Considering compatible theory of these indexes, the design method of non-fragile fault tolerant controller is proposed. Applying neural network to identification, location and diagnosis of faults, with consideration of multi-model reference method, a design method of active fault tolerant control is proposed.
(3) Fault tolerant control problems of two class interval systems are presented. Normal and time-delayed interval systems are comprehensively considered, the uncertain systems with fault of actuator are transformed into interval systems, and the fault tolerant problems of uncertain systems are solved with the theory of interval systems. Applying LMI, the inequality problems corresponding to the constraints of performance indexes are transformed to convex optimization problems, and the controller satisfying performance indexes are obtained by solving LMI with Matlab.
(4) Fault tolerant control problems under multiple constraints of several kinds of T-S fuzzy systems are studied. One kind of problems is for nonlinear systems described by T-S fuzzy model. The uncertainty of global fuzzy model and the fault of actuator are comprehensively considered, and an idea of fuzzy cost guaranteed fault tolerant control is proposed. The fuzzy control problems are transformed into convex optimization problems with LMI, and an expression of fuzzy H_∞cost guaranteed fault tolerant controller is given. The other kind of problems is about T-S fuzzy singular systems. Under the precondition of quadratic stability, considering H_2 & H_∞performance of system and the design of fault tolerant controller under the constraints of mixed indexes, the quadratic stability, excellent dynamic performance and steady performance of closed-loop fuzzy linear singular systems are ensured .
(5) Fault tolerant control of nonlinear systems under multi-index constraints is discussed. In practice, the uncertain parts are norm-bounded, and the nonlinear parts often enjoy the linearly bounded constraints, a design method of fault tolerant controller under multi-index constraints is proposed. H_∞cost guaranteed fault tolerant control of a class of complex uncertain nonlinear systems with time delay is discussed by means of LMI and Lyapunov stability theory. The existing conditions of H_∞cost guaranteed control rules and design methods of controller are given with LMI. The problems of non-fragile H_∞cost guaranteed control of system, when the faults of actuators and perturbations of controller parameters occur, are comprehensively considered in research process. The corresponding existing conditions of non-fragile cost guaranteed fault tolerant control rules, and the design methods of non-fragile cost guaranteed controller are given. The problem of chaos synchronization of chaotic systems with multiple time-delays is discussed by employing the state-feedback controller with memory, and a design approach of nonlinear controller is given for more complicated systems in structure.
Finally, the existing problems in this dissertation are discussed, and directions of further researches are pointed out.
(1)提出了不确定广义系统和不确定时滞广义系统在区域极点指标、H_∞指标、方差上界指标及保成本指标约束条件下的满意容错控制器设计方法及滤波器设计方法。在执行器故障条件下,利用线性矩阵不等式(LMI,Linear matrix inequality)分析了相容指标的取值范围和多指标约束下容错控制器存在的充分条件,并给出控制器的设计方法。
(2)针对不确定线性系统和线性系统族,提出了非脆弱容错控制设计方法。在考虑控制器不确定性的情况下,给出了一种综合区域极点约束、最小方差上界约束和H_∞约束的非脆弱容错控制设计方法,并分析了三种指标的相容性;同时又提出了一种主动容错控制设计方法。通过神经网络对故障进行辨识、定位和诊断,结合多模型参考方法,给出了一种主动容错控制设计方法。
(3)针对无时滞和带有时滞的两类区间系统,给出了各自的容错控制器设计方法。将带有执行器故障的不确定系统转化为区间系统,应用区间系统的相关理论解决了不确定系统的容错控制问题。应用LMI把相关性能指标约束对应的不等式问题转化为凸优化问题,最后通过解线性矩阵不等式,得到满足性能指标要求的控制器。
(4)提出了两类T-S模糊系统的多指标约束容错控制设计方法。一类是T-S模糊状态时滞系统,并综合考虑全局模糊模型的不确定性和执行器故障,提出了一种模糊H_∞保成本容错控制的思想,并利用LMI把相应的模糊控制问题转化成凸优化问题,给出了模糊H_∞保成本容错控制器的表达式。另一类是针对T-S模糊广义系统,在保证其二次稳定的前提条件下,兼顾系统的H_2和H_∞性能混合指标约束下的容错控制器设计问题,保证了整个闭环模糊非线性广义系统的二次稳定性和良好的动态品质和稳态性能。
(5)针对不确定部分具有范数有界约束,非线性部分满足线性有界约束的不确定非线性系统,提出了一种多指标约束条件下的容错控制器设计方法。利用LMI结合Lyapunov稳定性理论研究了一种复杂的不确定非线性时滞系统的H_∞保成本容错控制问题。综合考虑了当系统的执行器发生故障和控制器参数发生摄动时,系统的非脆弱H_∞保成本控制问题,给出了非脆弱H_∞保成本容错控制律的存在条件和设计方法;同时应用有记忆状态反馈控制器,提出了多时滞混沌系统的H_∞混沌同步控制设计方法,对于模型结构发生变化,输入改变的情况,又给出了一种非线性容错控制器的设计方法。
最后,指出了本文中还存在的问题和需要进一步探讨的研究方向。
Fault tolerant control is a novel strategy to improve the security and reliability of systems. Its meaning is that dynamical systems can run safely under the acceptable dynamical and stable performances when the faults of dynamic systems occur. Now, the study on fault tolerant control under multi-index constraints is still in primary stage, the results are mainly for normal linear systems. Based on the above consideration, this dissertation consider singular systems, interval systems and non-linear systems, study the fault tolerant control problems for them under the constraints of multiple indexes, propose the satisfactory fault tolerant control for them , deduce the existing conditions and design method of non-fragile satisfactory fault tolerant controller, so as to improve the fault tolerant control theory under multi-index constraints, thus provide a theoretical backbone for its engineering applications. The principal research results and innovations are outlined as follows:
(1) The design methods of satisfactory fault tolerant controllers and filters of uncertain singular systems, along with its time-delayed versions, are proposed, comprehensively considering regional pole index, H_∞constraint, variance upper bound and cost guaranteed constraint. We adopt the fault model of actuator, analyze the value ranges of compatible indexes and sufficient conditions for the existing of fault tolerant controller under the constraint of multiple indexes, and a constructive design method of controller is given.
(2) The problem of non-fragile fault tolerant control of uncertain linear system and linear system famlies are proposed, with the consideration of uncertainty of controllers. The regional pole index, minimal variance upper bound index and H_∞index are considered comprehensively. Considering compatible theory of these indexes, the design method of non-fragile fault tolerant controller is proposed. Applying neural network to identification, location and diagnosis of faults, with consideration of multi-model reference method, a design method of active fault tolerant control is proposed.
(3) Fault tolerant control problems of two class interval systems are presented. Normal and time-delayed interval systems are comprehensively considered, the uncertain systems with fault of actuator are transformed into interval systems, and the fault tolerant problems of uncertain systems are solved with the theory of interval systems. Applying LMI, the inequality problems corresponding to the constraints of performance indexes are transformed to convex optimization problems, and the controller satisfying performance indexes are obtained by solving LMI with Matlab.
(4) Fault tolerant control problems under multiple constraints of several kinds of T-S fuzzy systems are studied. One kind of problems is for nonlinear systems described by T-S fuzzy model. The uncertainty of global fuzzy model and the fault of actuator are comprehensively considered, and an idea of fuzzy cost guaranteed fault tolerant control is proposed. The fuzzy control problems are transformed into convex optimization problems with LMI, and an expression of fuzzy H_∞cost guaranteed fault tolerant controller is given. The other kind of problems is about T-S fuzzy singular systems. Under the precondition of quadratic stability, considering H_2 & H_∞performance of system and the design of fault tolerant controller under the constraints of mixed indexes, the quadratic stability, excellent dynamic performance and steady performance of closed-loop fuzzy linear singular systems are ensured .
(5) Fault tolerant control of nonlinear systems under multi-index constraints is discussed. In practice, the uncertain parts are norm-bounded, and the nonlinear parts often enjoy the linearly bounded constraints, a design method of fault tolerant controller under multi-index constraints is proposed. H_∞cost guaranteed fault tolerant control of a class of complex uncertain nonlinear systems with time delay is discussed by means of LMI and Lyapunov stability theory. The existing conditions of H_∞cost guaranteed control rules and design methods of controller are given with LMI. The problems of non-fragile H_∞cost guaranteed control of system, when the faults of actuators and perturbations of controller parameters occur, are comprehensively considered in research process. The corresponding existing conditions of non-fragile cost guaranteed fault tolerant control rules, and the design methods of non-fragile cost guaranteed controller are given. The problem of chaos synchronization of chaotic systems with multiple time-delays is discussed by employing the state-feedback controller with memory, and a design approach of nonlinear controller is given for more complicated systems in structure.
Finally, the existing problems in this dissertation are discussed, and directions of further researches are pointed out.
引文
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