不确定双曲型分布参数系统控制分析与设计

发布时间：2018-05-31 06:11

本文选题：双曲型分布参数系统 + PDE-ODE级联系统　；参考：《山东大学》2016年博士论文

【摘要】：实际工程中,许多动态过程都可建模为双曲型分布参数系统,例如：弦的振动、人口的发展、起重机的物料吊运、水体的流动、石油和天然气的开采和管道运输等.与集中参数系统(由常微分方程描述)相比,分布参数系统(由偏微分方程描述)可以更精确、更全面的刻画实际系统的动态,但由于其状态空间的无穷维特性及系统本身的复杂性,使得许多在集中参数系统中已经得到很好解决的控制问题仍然是分布参数系统中具较大挑战性的难题.此外,实际中,由于对被控对象工作机理认识不清、测量工具精度不够或受外部扰动影响,系统不可避免地存在不确定性/未知性,这使得控制分析与设计更加复杂,已有的针对确定系统发展的控制方法不再适用.因此,研究不确定双曲型分布参数系统控制具有重要的理论价值和实际意义.本文针对几类不确定双曲型分布参数系统,研究其状态反馈／输出反馈边界镇定问题.通过利用自适应技术、时变技术、反推方法、LaSalle不变原理,算子半群理论以及Lyapunov稳定性理论,提出了多种边界控制策略及适定性和稳定性分析方法.与已有结果相比,本文所研究的系统容许更严重不确定性／未知性,本质放宽了对系统的限制,拓展了已有方法的适用范围,完善了分布参数系统控制理论.此外,本文所发展的边界控制策略可为其它控制问题提供借鉴和指导.本文的主要研究内容包括如下四部分：一、带有未知空间变参数的一阶双曲型PDE系统的自适应边界镇定该部分内容是本文的第三章,主要研究了一类带有未知空间变参数的一阶双曲型PDE系统的自适应边界镇定问题.已有相关文献不容许带有未知参数或未知空间变参数,因此,所研究的系统具有更严重的不确定性／未知性,这使得已有方法无效.为解决该问题,首先,通过运用无穷维反推方法、自适应技术和投影算子,成功地给出一个动态补偿器来补偿系统主方程带有的强未知性.然后,借助确定等价原理构造出状态反馈边界控制器,并利用Lyapunov稳定性理论证明了所构造的控制器可以镇定原系统.二、带有谐波扰动的PDE-ODE级联系统的自适应状态反馈镇定该部分内容是本文的第四章,主要研究了一类带有不确定输入谐波扰动的二阶双曲型PDE-ODE级联系统的自适应边界镇定问题.已有相关文献中所考虑的系统要么不允许存在扰动要么扰动被限制在一个已知区间,而本文所研究系统带有的扰动属于一个未知区间,这使得本文所研究的问题更符合实际.为解决该问题,首先,结合自适应技术和针对集中参数系统发展的反推方法,成功地构造出状态反馈边界控制器.然后,利用算子半群理论和LaSalle不变原理,严格证明了所得闭环系统的适定性和渐近稳定性.此外,还证明了控制器中所涉及的参数估计值最终均收敛到未知参数的真实值.三、不确定PDE-ODE级联系统的自适应输出反馈镇定该部分内容是本文的第五章和第六章.其中,第五章主要研究了一类带有不确定输入谐波扰动的PDE-ODE级联系统的自适应输出反馈镇定.与第四章本质不同的是,本章所研究系统不要求所有状态信息可用,因此更符合实际,所发展的自适应反馈控制策略适用范围更广.首先,通过引入一个观测器估计原系统的不可测状态.在此基础上,借助自适应技术和针对集中参数系统所发展的反推方法,成功地构造出输出反馈边界控制器.然后,利用算子半群理论和LaSalle不变原理分析得到闭环系统的适定性和渐近稳定性,并且还得到所有参数的估计值最终均收敛到未知参数的真实值.第六章主要研究了一类同时带有不确定参数和输入谐波扰动的PDE-ODE级联系统的自适应输出反馈控制问题.与第五章本质不同的是,本章所考虑的系统除了带有不确定输入谐波扰动外,还允许带有上下界未知的参数,并且可用于控制设计的信息更少.通过构造状态观测器,并利用自适应技术和反推方法,成功地设计出输出反馈边界控制器,确保了闭环系统的适定性和稳定性,并且保证了所有参数的估计值最终均收敛到未知参数的真实值.四、带有非周期时变输入扰动的PDE-ODE级联系统的输出反馈镇定该部分内容为本文的第七章,主要研究了一类带有非周期时变输入扰动的PDE-ODE级联系统的输出反馈控制问题.与第六章本质不同的是,本章所考虑系统带有的扰动并不限制是周期扰动,只要求有界且上下界可以未知.这使得控制器设计更加复杂,并且已有的系统性能分析方法不再适用.首先,通过引入一个时变状态观测器估计原系统的不可测状态.在此基础上,基于时变技术和反推方法构造了其干扰属于未知区间时的输出反馈边界控制器,并利用Lyapunov稳定性理论证明了所构造的控制器可以镇定原系统.
[Abstract]:In practical engineering, many dynamic processes can be modeled as hyperbolic distributed parameter systems, such as the vibration of the chord, the development of the population, the lifting of the crane material, the flow of the water body, the exploitation of oil and natural gas, and the pipeline transportation. Compared with the centralized parameter system (ordinary differential Cheng Miaoshu), the distributed parameter system is described by the partial differential equation. ) it is more accurate and more comprehensive to describe the dynamic of the actual system, but because of the infinite dimension characteristics of the state space and the complexity of the system itself, many of the control problems that have been well solved in the centralized parameter system are still a challenging problem in the distributed parameter system. In addition, in practice, the controlled object is due to the controlled object. The understanding of working mechanism is not clear, the accuracy of measuring tools is not enough or influenced by external disturbance, the system inevitably has uncertainty / uncertainty, which makes the control analysis and design more complex, and the existing control methods for determining the development of the system are no longer applicable. Therefore, it is important to study the control of the uncertain hyperbolic distributed parameter system. In this paper, the problem of state feedback / output feedback boundary stabilization is studied for several types of uncertain hyperbolic distributed parameter systems. By using adaptive technology, time-varying technology, backstepping method, LaSalle invariance principle, operator semigroup theory and Lyapunov stability theory, a variety of boundary control strategies and adaption are proposed. Qualitative and stability analysis methods. Compared with the existing results, the system studied in this paper allows more serious uncertainty / uncertainty, relaxes the limitation to the system in essence, expands the scope of application of existing methods and improves the distribution parameter system control theory. In addition, the boundary control strategy developed in this paper can be proposed for other control problems. The main research contents of this paper include the following four parts: first, the adaptive boundary stabilization of the first order hyperbolic PDE system with unknown spatial variable parameters is the third chapter of this paper, and the problem of adaptive boundary stabilization for a class of first order double curved PDE systems with unknown space variable parameters is studied. The related literature is not allowed to have unknown parameters or unknown parameters. Therefore, the system has more serious uncertainty / unknown, which makes the existing methods invalid. In order to solve the problem, first, by using the infinite dimensional inverse method, adaptive technology and projection operator, a dynamic compensator is successfully given to compensate for the problem. The strong unknown of the system's principal equation. Then, the state feedback boundary controller is constructed by determining the equivalence principle, and the Lyapunov stability theory is used to prove that the constructed controller can stabilize the original system. Two, the adaptive state feedback of the PDE-ODE cascade system with harmonic disturbance is the fourth chapter of this article. The problem of adaptive boundary stabilization for a class of two order hyperbolic PDE-ODE cascade systems with uncertain input harmonic disturbances is studied. The systems considered in the related literature either do not allow the existence of disturbances or disturbances to be restricted to a known interval, and the disturbances in this paper belong to an unknown interval. In order to solve the problem, in order to solve the problem, first of all, the state feedback boundary controller is constructed by combining the adaptive technique and the backstepping method for the development of the centralized parameter system. Then, using the operator semigroup theory and the LaSalle invariance principle, Yan Ge proves the well posed and asymptotical stability of the closed loop system. In addition, it is also proved that the parameters involved in the controller ultimately converge to the true values of the unknown parameters. Three, the adaptive output feedback of the uncertain PDE-ODE cascade system is the fifth chapter and the sixth chapter of this paper. Among them, the fifth chapter mainly studies a class of PDE-ODE with uncertain input harmonic disturbances. The adaptive output feedback stabilization of cascaded systems is different from the fourth chapter. The system does not require all state information to be used in this chapter, so the adaptive feedback control strategy is more applicable. First, an observer is introduced to estimate the unmeasurable state of the original system. The adaptive technology and the backstepping method developed for the centralized parameter system have successfully constructed the output feedback boundary controller. Then, by using the operator semigroup theory and the LaSalle invariance principle, the well posed and asymptotical stability of the closed loop system are obtained, and the estimated values of all the parameters are finally converged to the truth of the unknown parameters. The sixth chapter mainly studies an adaptive output feedback control problem for a class of PDE-ODE cascaded systems with uncertain parameters and input harmonic disturbances. Unlike the fifth chapter, the system considered in this chapter is allowed to take the unknown parameters of the upper and lower bounds, and can be used for control in addition to the uncertain input harmonic disturbances. The information of the design is less. By constructing the state observer and using the adaptive technology and the backstepping method, the output feedback boundary controller is successfully designed to ensure the adaptability and stability of the closed loop system, and the estimated values of all the parameters are finally converged to the true values of the unknown parameters. Four, with the non periodic time-varying input. The output feedback of the disturbed PDE-ODE cascade system is composed of the seventh chapter of this paper. The output feedback control problem of a class of PDE-ODE cascaded systems with aperiodic time-varying input disturbance is mainly studied. Unlike the sixth chapter, the disturbance considered by the system in this chapter is not limited to periodic disturbances and only requires that The boundary and upper and lower bounds can be unknown. This makes the design of the controller more complex and the existing system performance analysis method is no longer applicable. First, a time-varying state observer is introduced to estimate the unmeasurable state of the original system. On this basis, the time-varying and backstepping methods are made to construct its output inverse when the interference belongs to the unknown interval. The feedback boundary controller is used, and the Lyapunov stability theory is used to prove that the constructed controller can stabilize the original system.
【学位授予单位】：山东大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP13

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