基于Markov跳变理论的网络控制系统研究
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摘要
网络技术的不断发展使得越来越多的控制系统将基于网络运行,从而出现了网络控制系统(Networked Control Systems,NCSs)。网络控制系统是指通过网络实现控制系统各元件(传感器、控制器、执行器等)之间信息(参考输入、被控对象输出、控制器输入等)交换的闭环反馈控制系统。网络在给控制系统带来众多优势(资源共享、减少系统布线、降低成本、交互性好、具有高的诊断能力、易于安装和维护、能有效提高系统可靠性等)的同时,网络中的延时、数据包丢失、带宽限制等问题也使控制系统的建模、分析和设计变得非常复杂。
本文结合鲁棒控制理论及Markov跳变理论,对具有随机时延、数据包丢失的网络控制系统进行合理地建模及统一建模。通过引入多种性能指标,研究了网络控制系统的稳定性及鲁棒性,从而建立系统性能指标与网络因素之间的内在联系。本文主要采用理论分析和数值仿真相结合的方法,研究具有随机时延、数据包丢失的离散时间网络控制系统的建模、稳定性分析及鲁棒控制等问题。
本文的研究内容主要包括以下四大部分:
第一部分(即第一章)首先介绍网络控制系统研究意义及存在的基本问题。其次介绍网络控制系统的研究历史及现状。最后就本文的主要工作及所涉及的符号作了必要的说明。
第二部分,(第二章)用两个相互独立的Markov链分别建模传感器与控制器、控制器与执行器之间随机的丢包。针对控制器与执行器之间随机丢包的Markov链状态难于获得的问题,基于隐Markov模型方法得到系统稳定的充分条件,给出最优控制器的设计方法。(第三章)采用增广矩阵的方法将传感器与控制器、控制器与执行器之间具有随机丢包的网络控制系统建模成四个子系统,四个子系统之间的切换遵循Markov跳变过程,基于Markov跳变理论,得到系统随机稳定的充分条件,并提出了控制器的设计方法。最后数值仿真验证方法的有效性及结果的正确性。
第三部分(即第四章)针对传感器与控制器、控制器与执行器之间具有随机Markov时延的网络控制系统的鲁棒控制问题(保性能控制、H∞控制、H 2 /H∞控制)。基于Markov跳变理论,该类系统被建模为多步Markov跳变线性系统,同时考虑系统受多种性能指标约束。基于Lyapunov稳定性定理及线性矩阵不等式求解方法得到闭环系统随机稳定的充分条件,并分别提出保性能控制器、H∞控制器、混合H_2 /H∞控制器的设计方法,简易倒立摆系统的仿真例子验证了所提方法的正确性及有效性。
第四部分(即第五章)针对传感器与控制器、控制器与执行器之间具有随机时延、丢包的网络控制系统的稳定、镇定问题。基于Markov跳变理论,该类系统被建模为具有Markov时延的Markov跳变线性系统。基于Lyapunov稳定性定理及线性矩阵不等式求解方法,得到该类系统随机稳定的充分条件,并分别提出状态反馈、输出反馈镇定控制器的设计方法,角位置系统的仿真例子验证了所提方法的正确性及有效性。
With the development of the network technology, more and more control systems will run based on network. Then the concept of networked control systems (NCSs) is proposed. NCSs are a type of closed-loop systems, in which the communication networks are employed to transmit information and control signals (reference input, plant output, control input, etc.) among control system components (sensors, controllers, actuators, etc.). The use of the communication networks brings many advantages such as sharing resources, reduced weight, lower cost, greater agility in diagnosis and maintenance, simple installation and maintenance, as well as high efficiency, flexibility and reliability. However, the communication networks in control loops also have some constraints such as time delays, packet dropouts and limited bandwidth, which complicate the analysis and design of NCSs.
In this dissertation, we address the modeling and unified model of NCSs with random time delays and packet dropouts under Markov jump theory and robust control theory. The stability and robust control problems are investigated by introducing kinds of performance indices. The networked quality and the inner relationship between performance indices are also established. In this paper, the modeling, stability and robust control problems of NCSs with random time delays and packet dropouts are investigated mainly by employing theoretical analysis and numerical simulation methods.
This paper contains four parts.
In the first part (Chapter 1), the research background and fundamental issues of networked control systems are firstly introduced briefly. Secondly, the research evolution of networked control systems are reviewed. Finally, the main work of this dissertation and the used notations are listed.
In the second part (Chapter 2, 3) the random sensor-to-controller (S-C) and controller-to-actuator (C-A) data packet dropouts are modeled by two independent Markov chains. The modeling and stochastic stability of NCSs are studied based on the hidden Markov model (HMM). Then the design of the optimal controller is given. Considering the random data packet dropouts occurring in the S-C and C-A, the resulting closed-loop NCS based on the extended matrix method is modeled as a discrete-time Markov jump linear system with four modes. Sufficient conditions ensuring the stochastic stability for NCS are established based on stochastic Lyapunov functions and linear matrix inequality (LMI) approach. Finally, the simulation examples illustrate the validity and feasibility of the results.
In the third part (Chapter 4), the robust control (guaranteed cost control、H∞control、H 2 /H∞control) for a class of discrete-time NCSs with Markov time delays is investigated. Networked control systems in the frame of Markov jump theory are modeled as multi-step Markovian jump linear systems. By introducing kinds of performance indices and co-considering the robustness and stability, the focus is on the design of the robust stabilization controller (guaranteed cost controller、H∞controller、H 2 /H∞controller) based on stochastic Lyapunov functional and LMI approach. Finally, the simulation examples illustrate the effectiveness of the results.
In the last part (Chapter 5), the stability and stabilization problems for discrete-time NCSs with random S-C and C-A time delays and packet dropouts are investigated. Networked control system with S-C and C-A time delays and packet dropouts is modeled as Markovian jump linear system with Markov delays. Based on Lyapunov stability theory and LMI method, sufficient conditions of the stochastic stability and stabilization controller design method for NCSs with random time delays and packet dropouts are presented. Finally, the numerical examples are given to illustrate the effectiveness of the results.
本文结合鲁棒控制理论及Markov跳变理论,对具有随机时延、数据包丢失的网络控制系统进行合理地建模及统一建模。通过引入多种性能指标,研究了网络控制系统的稳定性及鲁棒性,从而建立系统性能指标与网络因素之间的内在联系。本文主要采用理论分析和数值仿真相结合的方法,研究具有随机时延、数据包丢失的离散时间网络控制系统的建模、稳定性分析及鲁棒控制等问题。
本文的研究内容主要包括以下四大部分:
第一部分(即第一章)首先介绍网络控制系统研究意义及存在的基本问题。其次介绍网络控制系统的研究历史及现状。最后就本文的主要工作及所涉及的符号作了必要的说明。
第二部分,(第二章)用两个相互独立的Markov链分别建模传感器与控制器、控制器与执行器之间随机的丢包。针对控制器与执行器之间随机丢包的Markov链状态难于获得的问题,基于隐Markov模型方法得到系统稳定的充分条件,给出最优控制器的设计方法。(第三章)采用增广矩阵的方法将传感器与控制器、控制器与执行器之间具有随机丢包的网络控制系统建模成四个子系统,四个子系统之间的切换遵循Markov跳变过程,基于Markov跳变理论,得到系统随机稳定的充分条件,并提出了控制器的设计方法。最后数值仿真验证方法的有效性及结果的正确性。
第三部分(即第四章)针对传感器与控制器、控制器与执行器之间具有随机Markov时延的网络控制系统的鲁棒控制问题(保性能控制、H∞控制、H 2 /H∞控制)。基于Markov跳变理论,该类系统被建模为多步Markov跳变线性系统,同时考虑系统受多种性能指标约束。基于Lyapunov稳定性定理及线性矩阵不等式求解方法得到闭环系统随机稳定的充分条件,并分别提出保性能控制器、H∞控制器、混合H_2 /H∞控制器的设计方法,简易倒立摆系统的仿真例子验证了所提方法的正确性及有效性。
第四部分(即第五章)针对传感器与控制器、控制器与执行器之间具有随机时延、丢包的网络控制系统的稳定、镇定问题。基于Markov跳变理论,该类系统被建模为具有Markov时延的Markov跳变线性系统。基于Lyapunov稳定性定理及线性矩阵不等式求解方法,得到该类系统随机稳定的充分条件,并分别提出状态反馈、输出反馈镇定控制器的设计方法,角位置系统的仿真例子验证了所提方法的正确性及有效性。
With the development of the network technology, more and more control systems will run based on network. Then the concept of networked control systems (NCSs) is proposed. NCSs are a type of closed-loop systems, in which the communication networks are employed to transmit information and control signals (reference input, plant output, control input, etc.) among control system components (sensors, controllers, actuators, etc.). The use of the communication networks brings many advantages such as sharing resources, reduced weight, lower cost, greater agility in diagnosis and maintenance, simple installation and maintenance, as well as high efficiency, flexibility and reliability. However, the communication networks in control loops also have some constraints such as time delays, packet dropouts and limited bandwidth, which complicate the analysis and design of NCSs.
In this dissertation, we address the modeling and unified model of NCSs with random time delays and packet dropouts under Markov jump theory and robust control theory. The stability and robust control problems are investigated by introducing kinds of performance indices. The networked quality and the inner relationship between performance indices are also established. In this paper, the modeling, stability and robust control problems of NCSs with random time delays and packet dropouts are investigated mainly by employing theoretical analysis and numerical simulation methods.
This paper contains four parts.
In the first part (Chapter 1), the research background and fundamental issues of networked control systems are firstly introduced briefly. Secondly, the research evolution of networked control systems are reviewed. Finally, the main work of this dissertation and the used notations are listed.
In the second part (Chapter 2, 3) the random sensor-to-controller (S-C) and controller-to-actuator (C-A) data packet dropouts are modeled by two independent Markov chains. The modeling and stochastic stability of NCSs are studied based on the hidden Markov model (HMM). Then the design of the optimal controller is given. Considering the random data packet dropouts occurring in the S-C and C-A, the resulting closed-loop NCS based on the extended matrix method is modeled as a discrete-time Markov jump linear system with four modes. Sufficient conditions ensuring the stochastic stability for NCS are established based on stochastic Lyapunov functions and linear matrix inequality (LMI) approach. Finally, the simulation examples illustrate the validity and feasibility of the results.
In the third part (Chapter 4), the robust control (guaranteed cost control、H∞control、H 2 /H∞control) for a class of discrete-time NCSs with Markov time delays is investigated. Networked control systems in the frame of Markov jump theory are modeled as multi-step Markovian jump linear systems. By introducing kinds of performance indices and co-considering the robustness and stability, the focus is on the design of the robust stabilization controller (guaranteed cost controller、H∞controller、H 2 /H∞controller) based on stochastic Lyapunov functional and LMI approach. Finally, the simulation examples illustrate the effectiveness of the results.
In the last part (Chapter 5), the stability and stabilization problems for discrete-time NCSs with random S-C and C-A time delays and packet dropouts are investigated. Networked control system with S-C and C-A time delays and packet dropouts is modeled as Markovian jump linear system with Markov delays. Based on Lyapunov stability theory and LMI method, sufficient conditions of the stochastic stability and stabilization controller design method for NCSs with random time delays and packet dropouts are presented. Finally, the numerical examples are given to illustrate the effectiveness of the results.
引文
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