具有多目标约束的不确定NCS鲁棒满意容错控制
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摘要
网络化控制系统（Network Control System，NCS）是将传感器、控制器以及执行器等通过网络连接而构成的闭环反馈控制系统。随着信息与控制技术的发展，控制系统规模不断扩大，复杂性日益提高，故障诱发因素也随之增多，因此，通过对系统进行容错设计，提高安全性和可靠性已成为刻不容缓的问题。近年来，对于不确定NCS的鲁棒容错控制研究尽管已取得不少成果，但绝大部分都是针对系统鲁棒完整性及鲁棒H_∞完整性进行的，对于不确定NCS多目标约束下的满意容错控制的研究还少有报道。在实际中，人们即使对故障NCS，所期望的指标也是多方面的，即在确保系统稳定的同时，还期求有良好的动、静态及干扰抑制等性能。但是NCS被动容错的保守性又成为多目标约束下控制器优化求解的屏障，因此如何减少结论保守性并提高NCS容错满意度，便成为容错控制领域既充满挑战又具有重要科学和工程意义的热点问题。
基于以上考虑，本文针对具有时变时延和丢包的线性不确定NCS，将丢包当做一种特殊时延，综合应用Lyapunov理论、更紧的积分不等式及LMI等技术，推证出了具有多目标约束的不确定NCS少保守性鲁棒满意容错设计准则，为其更好的应用于工程实际提供了理论依据，主要工作包括：
1）基于状态反馈的不确定NCS鲁棒满意容错控制研究
针对具有时变时延和丢包的线性不确定NCS，采用状态反馈控制策略，通过构造适当的时滞依赖Lyapunov-Krasovskii泛函，借助于积分不等式等方法，考虑可能的执行器或传感器失效故障，推证出了系统在α-稳定约束下的鲁棒容错、鲁棒H_∞容错及鲁棒广义H_2/H_∞容错判别准则，并以LMIs的方式给出了控制器的求解和优化方法。
2）基于动态输出反馈的不确定NCS鲁棒满意容错控制研究
针对具有时变时延和丢包的线性不确定NCS，采用动态输出控制策略，在对时延进行分段处理的情形下，通过构造适当的时滞依赖Lyapunov-Krasovskii泛函，借助于积分不等式等方法，考虑可能的执行器或传感器失效故障，推证出了系统在α-稳定约束下的鲁棒容错、鲁棒H_∞容错及鲁棒广义H_2/H_∞容错判别准则，并以LMIs的方式给出了控制器的求解和优化方法。
3）控制器设计的正确性、有效性验证及结论保守性分析
对于上述研究结论，以仿真算例验证了其正确性和有效性，结果表明文中所述方法是正确且可行的，多目标约束条件的引入，进一步提高了NCS的容错满意度。此外，还对本文与前期研究结果进行了保守性的比较分析，结果表明，由于未进行模型转换及较紧积分不等式的应用，使本文所述方法具有较小的保守性，这无疑为NCS容错满意度的提高增加了求解空间。同时在证明过程中未引入任何自由权矩阵，降低了计算复杂度，使控制器的设计更加便利。
The Networked Control System (NCS) is a closed-loop feedback Control Systemwhich constituted with sensors, actuators and controllers through the network. Alongwith the development of information and control technology, the control system scalecontinues to expand, complexity is increasing day by day, fault inducing factors alsoincreases. Therefore, how to improve the systems safety and reliability through thefault tolerant design have become the urgent problems. In recent years, for uncertaintyNCS robust fault-tolerant control research although have made some results, but mostare for the system robust integrity and robust H_∞integrity, for uncertainty NCSsatisfacory fault-tolerant control also have rare reported. In actual, even if the systemfails, people also expect index is multifaceted. Namely in the ensure of the stability ofthe system at the same time, also have a good dynamic,static and disturbing resistanceperformances and so on. But the conservative of NCS passive fault tolerant becomethe barrier for optimization controller with multi-indices constraints.So how to reducethe conclusion conservative and improve the NCS fault-tolerant satisfaction make thefault-tolerant control field that is both a challenging and profound scientificsignificance.
Based on the above consideration, this paper aimed at a linear uncertainty NCSwith time-varying delay and lost package, packet-dropout is regarded as a special kindof delay.General use Lyapunov theory, more tight integral inequalities and LMItechnology, the less conservative robust satisfactory fault-tolerant design criterionwith more target constraint for uncertainty NCS was put forward. This is dotheoretical foil for its better applied to engineering practice, the main work include:
1) Robust satisfactory fault-tolerant control research for uncertainty NCS basedon state feedback
For a linear uncertainty NCS with time-varying delay and lost package, using thestate feedback control strategy, by construct a proper delay-dependent Lyapunov-Krasovskii functional and by means of integral inequality, the criterions are obtaintedfor system with robust fault tolerant, robust H_∞fault tolerantand robustgeneralizedH_2/H_∞fault toleran constraints on α-stability. And via LMIs controllersolution and optimization method were given.
2) Robust satisfactory fault-tolerant control research for uncertainty NCS basedon dynamic output feedback
For a linear uncertainty NCS with time-varying delay and lost package, using thedynamic output feedback control strategy and segment handling to delay, by constructa proper delay-dependent Lyapunov-Krasovskii functional,and useing integral inequality,the criterions are obtainted for system with robust fault tolerant,robust H∞fault tolerantand robust generalizedH2/H∞fault toleran constraints on α-stability.And via LMIs controller solution and optimization method were given.
3) Correctness and effectiveness validation for controller and Conclusionconservative analysis
For the above research conclusion, with an example to verify its accuracy andeffectiveness, and the results show that the method is correct and feasible,also theintroduction of multi-objective constraint conditions further improve the tolerancesatisfaction of the NCS. Besides, also have a conservative comparative analysis onthis article and the earlier results, the results show that because not make modeltransformation and use tight integral inequality, make the methods described in thispaper have small conservative. There is no doubt that the increase of the satisfactiondegree of the NCS fault tolerance for the solution to the space. At the same time in theProve process not introduce any free weighting matrix, which not only further reducedthe system conservative, but also reduce the computational complexity.
基于以上考虑，本文针对具有时变时延和丢包的线性不确定NCS，将丢包当做一种特殊时延，综合应用Lyapunov理论、更紧的积分不等式及LMI等技术，推证出了具有多目标约束的不确定NCS少保守性鲁棒满意容错设计准则，为其更好的应用于工程实际提供了理论依据，主要工作包括：
1）基于状态反馈的不确定NCS鲁棒满意容错控制研究
针对具有时变时延和丢包的线性不确定NCS，采用状态反馈控制策略，通过构造适当的时滞依赖Lyapunov-Krasovskii泛函，借助于积分不等式等方法，考虑可能的执行器或传感器失效故障，推证出了系统在α-稳定约束下的鲁棒容错、鲁棒H_∞容错及鲁棒广义H_2/H_∞容错判别准则，并以LMIs的方式给出了控制器的求解和优化方法。
2）基于动态输出反馈的不确定NCS鲁棒满意容错控制研究
针对具有时变时延和丢包的线性不确定NCS，采用动态输出控制策略，在对时延进行分段处理的情形下，通过构造适当的时滞依赖Lyapunov-Krasovskii泛函，借助于积分不等式等方法，考虑可能的执行器或传感器失效故障，推证出了系统在α-稳定约束下的鲁棒容错、鲁棒H_∞容错及鲁棒广义H_2/H_∞容错判别准则，并以LMIs的方式给出了控制器的求解和优化方法。
3）控制器设计的正确性、有效性验证及结论保守性分析
对于上述研究结论，以仿真算例验证了其正确性和有效性，结果表明文中所述方法是正确且可行的，多目标约束条件的引入，进一步提高了NCS的容错满意度。此外，还对本文与前期研究结果进行了保守性的比较分析，结果表明，由于未进行模型转换及较紧积分不等式的应用，使本文所述方法具有较小的保守性，这无疑为NCS容错满意度的提高增加了求解空间。同时在证明过程中未引入任何自由权矩阵，降低了计算复杂度，使控制器的设计更加便利。
The Networked Control System (NCS) is a closed-loop feedback Control Systemwhich constituted with sensors, actuators and controllers through the network. Alongwith the development of information and control technology, the control system scalecontinues to expand, complexity is increasing day by day, fault inducing factors alsoincreases. Therefore, how to improve the systems safety and reliability through thefault tolerant design have become the urgent problems. In recent years, for uncertaintyNCS robust fault-tolerant control research although have made some results, but mostare for the system robust integrity and robust H_∞integrity, for uncertainty NCSsatisfacory fault-tolerant control also have rare reported. In actual, even if the systemfails, people also expect index is multifaceted. Namely in the ensure of the stability ofthe system at the same time, also have a good dynamic,static and disturbing resistanceperformances and so on. But the conservative of NCS passive fault tolerant becomethe barrier for optimization controller with multi-indices constraints.So how to reducethe conclusion conservative and improve the NCS fault-tolerant satisfaction make thefault-tolerant control field that is both a challenging and profound scientificsignificance.
Based on the above consideration, this paper aimed at a linear uncertainty NCSwith time-varying delay and lost package, packet-dropout is regarded as a special kindof delay.General use Lyapunov theory, more tight integral inequalities and LMItechnology, the less conservative robust satisfactory fault-tolerant design criterionwith more target constraint for uncertainty NCS was put forward. This is dotheoretical foil for its better applied to engineering practice, the main work include:
1) Robust satisfactory fault-tolerant control research for uncertainty NCS basedon state feedback
For a linear uncertainty NCS with time-varying delay and lost package, using thestate feedback control strategy, by construct a proper delay-dependent Lyapunov-Krasovskii functional and by means of integral inequality, the criterions are obtaintedfor system with robust fault tolerant, robust H_∞fault tolerantand robustgeneralizedH_2/H_∞fault toleran constraints on α-stability. And via LMIs controllersolution and optimization method were given.
2) Robust satisfactory fault-tolerant control research for uncertainty NCS basedon dynamic output feedback
For a linear uncertainty NCS with time-varying delay and lost package, using thedynamic output feedback control strategy and segment handling to delay, by constructa proper delay-dependent Lyapunov-Krasovskii functional,and useing integral inequality,the criterions are obtainted for system with robust fault tolerant,robust H∞fault tolerantand robust generalizedH2/H∞fault toleran constraints on α-stability.And via LMIs controller solution and optimization method were given.
3) Correctness and effectiveness validation for controller and Conclusionconservative analysis
For the above research conclusion, with an example to verify its accuracy andeffectiveness, and the results show that the method is correct and feasible,also theintroduction of multi-objective constraint conditions further improve the tolerancesatisfaction of the NCS. Besides, also have a conservative comparative analysis onthis article and the earlier results, the results show that because not make modeltransformation and use tight integral inequality, make the methods described in thispaper have small conservative. There is no doubt that the increase of the satisfactiondegree of the NCS fault tolerance for the solution to the space. At the same time in theProve process not introduce any free weighting matrix, which not only further reducedthe system conservative, but also reduce the computational complexity.
引文
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