网络控制系统中控制与调度的协同设计
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摘要
随着网络控制系统研究的深入,网络控制系统中的网络调度逐渐受到研究者的重视,研究网络控制系统调度的目的是改善网络的QoS,减少冲突、阻塞等不利因素的发生,从而减小网络诱导时延,减少数据包丢失的发生,对于改善网络控制系统的性能具有重要的意义。但是网络和控制两方面存在着相互影响、相互制约的内在联系,解决上述问题应考虑控制与调度的协同设计,以保证网络的服务质量QoS和控制系统的控制质量QoC。
控制与调度的协同设计过程,需要从理论上研究调度对于控制系统性能的影响,从而为调度方法的确定提供依据。为了分析控制系统的各种性能,建立了输入、输出端都具有通信约束的通用NCS调度模型,并利用通信序列来表示调度情况,然后将其转化为离散切换系统。
在研究NCS调度模型的能控性、能观性时,利用循环不变子空间理论及其相关的性质,给出了静态调度下网络控制系统能控性、能观性的充要条件,并给出了原有控制系统与经由网络静态调度后系统之间能控性、能观性的关系。
利用切换系统中的多Lyapunov函数方法,对状态反馈下的NCS调度模型的稳定性、鲁棒性进行分析,并以LMI形式给出系统满足鲁棒性能的充要条件,及其鲁棒H∞控制器的设计方法;然后,对多系统调度的网络控制系统进行建模,将其也转化为离散切换系统,并将得到的鲁棒性相关结论,扩展到多系统调度中。
在状态反馈下对NCS调度模型展开保性能分析,以LMI形式给出系统保性能的充要条件,及其保性能控制律的求解;在此基础上,进一步得出最优保性能控制律的求解条件;然后将得到的结论推广到多系统调度中。
针对NCS中的调度,提出基于RM和EDF的二维调度策略,能够实现优先级与带宽的二级分配,具有较高的灵活性;并利用RM与EDF方法的任务可调度性条件,得出二维调度中的带宽可调度性条件;二维网络调度策略可以在同一个网络中,用RM及EDF调度方法来分别对不同的任务进行调度。
采样周期是QoC与QoS之间的纽带,在控制与调度协同设计中起到重要的作用,所以有必要从理论与实际应用两个角度出发对NCS中变采样进行研究。首先将NCS中的变采样建模为离散切换系统,再应用上面得到的鲁棒性能的有关结论就可以得出相关变采样H∞控制器的设计;其次在应用上,提出基于LS-SVM的在线网络预测控制,在LS-SVM的基础上,利用训练数据窗及训练数据阈值,推导出适合NCS的在线训练方法,结合GPC方法得到在线LS-SVM预测控制量的方程解。仿真结果显示,该方法可以很好的应对NCS中出现的时延、丢包以及变采样周期问题,且具有较好的鲁棒性。
With the development of NCS (Networked Control System), more and more researchers focus on the scheduling of network which can improve the QoS (Quality of Service) of network and reduce the chance of collision and Congestion in network, then it can reduce the network induce time delay and the rate of data packet loss, so scheduling has great signification on improving the performance of NCS. For network and control system having effect and restriction on each other, the method of control and scheduling co-design is the best way to solve this problem, which can guarantee the QoS of network and the QoC (Quality of Control) of control system.
The process of control and scheduling co-design needs to study the performance of control system affected by scheduling in theory, which can support to choose the method of scheduling. To analyze the performance of control system, the model of NCS scheduling is established with communication constrain both in its input and output channel, which can be transform into discrete-time switched system by expressing the status of scheduling as communication sequence.
On studying the controllability and observability of the model, utilizing the theory of recursive invariant subspace and its character, a necessary and sufficient condition is deduced for the controllability and observability of the model under static scheduling, what's more the relation of NCS's controllability and observability is presented between before and after the static scheduling.
The stability and robustness of the model are analyzed under state feedback by utilizing the method of multiple Lyapunov function, then the necessary and sufficient condition of the robustness is presented via LMI (Linear Matrix Inequality) and the method of designing H∞controller also is presented. The results are extended to the scheduling of multi-system which is modeled as above.
Under state feedback, the guaranteed cost control of the model is studied, and its necessary and sufficient condition is obtained. The method of solving guaranteed cost controller is deduced too, based on which the same of optimal guaranteed cost control is investigated and extended to the multi-system.
Based on RM(Rate Monotonic) and EDF(Earliest Deadline First),the two-dimension scheduling strategy is proposed to deal with the scheduling in NCS, which can realize to distribute priority and bandwidth in two level, and the condition of bandwidth schedulability is obtained based on the task schedulability of RM and EDF. This strategy can utilize RM and EDF to schedule different task in the same network.
The sampling period is linker between QoC and QoS, which plays a important role in control and scheduling co-design. So it is necessary to study variable-sampling from the standpoint of theory and application in NCS. In theory, the variable-sampling is modeled as discrete-time switched system, then the results of robustness obtained above is applied to it to get the method of H∞controller designing in variable-sampling NCS. From the application, an online network predictive control method based on LS-SVM (Least Squares Support Vector Machine) is proposed. Utilizing training data window and training data throuhold, an online training method which adapts to NCS is developed based on LS-SVM. The solution of control variable can be solved by integrating the method of GPC (Generalized Predictive Control). The results of simulation show that the method is robust to deal with the problem of time-delay, packet loss and variable-sampling in NCS.
控制与调度的协同设计过程,需要从理论上研究调度对于控制系统性能的影响,从而为调度方法的确定提供依据。为了分析控制系统的各种性能,建立了输入、输出端都具有通信约束的通用NCS调度模型,并利用通信序列来表示调度情况,然后将其转化为离散切换系统。
在研究NCS调度模型的能控性、能观性时,利用循环不变子空间理论及其相关的性质,给出了静态调度下网络控制系统能控性、能观性的充要条件,并给出了原有控制系统与经由网络静态调度后系统之间能控性、能观性的关系。
利用切换系统中的多Lyapunov函数方法,对状态反馈下的NCS调度模型的稳定性、鲁棒性进行分析,并以LMI形式给出系统满足鲁棒性能的充要条件,及其鲁棒H∞控制器的设计方法;然后,对多系统调度的网络控制系统进行建模,将其也转化为离散切换系统,并将得到的鲁棒性相关结论,扩展到多系统调度中。
在状态反馈下对NCS调度模型展开保性能分析,以LMI形式给出系统保性能的充要条件,及其保性能控制律的求解;在此基础上,进一步得出最优保性能控制律的求解条件;然后将得到的结论推广到多系统调度中。
针对NCS中的调度,提出基于RM和EDF的二维调度策略,能够实现优先级与带宽的二级分配,具有较高的灵活性;并利用RM与EDF方法的任务可调度性条件,得出二维调度中的带宽可调度性条件;二维网络调度策略可以在同一个网络中,用RM及EDF调度方法来分别对不同的任务进行调度。
采样周期是QoC与QoS之间的纽带,在控制与调度协同设计中起到重要的作用,所以有必要从理论与实际应用两个角度出发对NCS中变采样进行研究。首先将NCS中的变采样建模为离散切换系统,再应用上面得到的鲁棒性能的有关结论就可以得出相关变采样H∞控制器的设计;其次在应用上,提出基于LS-SVM的在线网络预测控制,在LS-SVM的基础上,利用训练数据窗及训练数据阈值,推导出适合NCS的在线训练方法,结合GPC方法得到在线LS-SVM预测控制量的方程解。仿真结果显示,该方法可以很好的应对NCS中出现的时延、丢包以及变采样周期问题,且具有较好的鲁棒性。
With the development of NCS (Networked Control System), more and more researchers focus on the scheduling of network which can improve the QoS (Quality of Service) of network and reduce the chance of collision and Congestion in network, then it can reduce the network induce time delay and the rate of data packet loss, so scheduling has great signification on improving the performance of NCS. For network and control system having effect and restriction on each other, the method of control and scheduling co-design is the best way to solve this problem, which can guarantee the QoS of network and the QoC (Quality of Control) of control system.
The process of control and scheduling co-design needs to study the performance of control system affected by scheduling in theory, which can support to choose the method of scheduling. To analyze the performance of control system, the model of NCS scheduling is established with communication constrain both in its input and output channel, which can be transform into discrete-time switched system by expressing the status of scheduling as communication sequence.
On studying the controllability and observability of the model, utilizing the theory of recursive invariant subspace and its character, a necessary and sufficient condition is deduced for the controllability and observability of the model under static scheduling, what's more the relation of NCS's controllability and observability is presented between before and after the static scheduling.
The stability and robustness of the model are analyzed under state feedback by utilizing the method of multiple Lyapunov function, then the necessary and sufficient condition of the robustness is presented via LMI (Linear Matrix Inequality) and the method of designing H∞controller also is presented. The results are extended to the scheduling of multi-system which is modeled as above.
Under state feedback, the guaranteed cost control of the model is studied, and its necessary and sufficient condition is obtained. The method of solving guaranteed cost controller is deduced too, based on which the same of optimal guaranteed cost control is investigated and extended to the multi-system.
Based on RM(Rate Monotonic) and EDF(Earliest Deadline First),the two-dimension scheduling strategy is proposed to deal with the scheduling in NCS, which can realize to distribute priority and bandwidth in two level, and the condition of bandwidth schedulability is obtained based on the task schedulability of RM and EDF. This strategy can utilize RM and EDF to schedule different task in the same network.
The sampling period is linker between QoC and QoS, which plays a important role in control and scheduling co-design. So it is necessary to study variable-sampling from the standpoint of theory and application in NCS. In theory, the variable-sampling is modeled as discrete-time switched system, then the results of robustness obtained above is applied to it to get the method of H∞controller designing in variable-sampling NCS. From the application, an online network predictive control method based on LS-SVM (Least Squares Support Vector Machine) is proposed. Utilizing training data window and training data throuhold, an online training method which adapts to NCS is developed based on LS-SVM. The solution of control variable can be solved by integrating the method of GPC (Generalized Predictive Control). The results of simulation show that the method is robust to deal with the problem of time-delay, packet loss and variable-sampling in NCS.
引文
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