线性时滞多智能体系统的最优控制研究

发布时间：2018-02-02 08:43

本文关键词： 代数图论时变时滞多智能体系统加权平均一致性线性矩阵不等式最优控制　出处：《西南交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：在工业生产中,设备的运行无法达到理想状态,时滞现象是控制过程中无法避免的问题之一。时滞系统的最优控制问题具有很高的研究价值和现实意义,也是近年来控制领域研究的热点和难点课题之一。一致性问题作为智能体之间协调合作的基础,受到越来越多研究者的关注。所谓"一致性"是指:智能体的某些状态变量从一组给定值经过一定的时间之后趋于同一值,称为系统的决策值。而一致性算法就是使得系统中每个智能体的状态趋于一致的协议。本文主要讨论了带有时滞的线性多智能体系统一致性和最优控制问题。本论文的主要内容和研究成果总结如下:1.主要对线性时变时滞多智能体网络的加权平均一致性问题进行了研究,通过将加权平均系数融合进控制器参数设计,大大方便了多智能体系统的综合。基于代数图论和矩阵分析工具,分别研究了时变时滞多智能体系统在固定和切换网络拓扑下的加权平均一致性,利用Lyapunov-Krasovskii理论,以LMI的形式给出了线性控制协议在网络拓扑是固定和切换两种情况下取得加权平均一致性的充分条件,结论证明所有的节点在实现稳定时均达到了智能体初态的加权平均值。2.研究了具有时滞的一般离散时间多智能体系统的一致性问题,基于李雅普诺夫稳定性定理,通过构造李雅普诺夫泛函并保留了李雅普诺夫泛函差分中的有用信息,利用线性矩阵不等式方法,给出了系统稳定的充分条件,并通过实例计算求出了系统能够容忍的时滞范围和满足系统稳定性条件的一组矩阵解,从而验证了本文所得到的结论的有效性和可行性。3.研究了线性时滞多智能体系统的最优控制问题。首先,针对时滞系统的最优状态调节问题,对于带时滞的状态方程,根据柯西公式的特性,求出了一个特解,给出了闭环系统的状态线性反馈控制律,并最终得到了最优控制器的解的形式。其次,针对时滞多智能体系统在有限时域下的最优跟踪问题,本文将含有输入时滞的线性系统变换成形式上无时滞的线性系统,根据最优控制理论构造了 Riccati矩阵方程组,并提出了动态输出反馈最优跟踪控制算法。最后,通过计算机仿真实例验证了本文结论的正确性和有效性。
[Abstract]:In the industrial production, the operation of the equipment can not reach the ideal state, and the delay phenomenon is one of the unavoidable problems in the control process. The optimal control problem of the time-delay system has high research value and practical significance. It is also one of the hot and difficult topics in the field of control in recent years. Consistency is the basis of coordination and cooperation among agents. More and more researchers pay attention to it. The so-called "consistency" means that some state variables of an agent tend to the same value after a certain time from a given set of values. This paper mainly discusses the consistency and optimal control of linear multi-agent systems with time delay. The main contents and research results are summarized as follows:. 1. The weighted average consistency problem of linear time-varying time-delay multi-agent networks is studied. By integrating the weighted average coefficient into the controller parameter design, the synthesis of multi-agent system is greatly facilitated, based on algebraic graph theory and matrix analysis tool. The weighted average consistency of time-varying time-delay multi-agent systems under fixed and switched network topology is studied, and the Lyapunov-Krasovskii theory is used. In the form of LMI, a sufficient condition is given for the linear control protocol to obtain weighted average consistency when the network topology is fixed and handoff. It is proved that all nodes reach the weighted average of the initial state of the agent. 2. The consistency problem of the general discrete-time multi-agent system with time delay is studied. Based on Lyapunov stability theorem, by constructing Lyapunov Functionals and preserving useful information in Lyapunov functional difference, a sufficient condition for the stability of the system is given by using the method of linear matrix inequality (LMI). A set of matrix solutions which can tolerate the delay range and satisfy the stability condition of the system are obtained by the example calculation. Therefore, the validity and feasibility of the conclusions obtained in this paper are verified. 3. The optimal control problem for linear time-delay multi-agent systems is studied. Firstly, the optimal state adjustment problem for time-delay systems is studied. For the state equation with time delay, according to the characteristic of Cauchy formula, a special solution is obtained, and the state linear feedback control law of the closed-loop system is given, and the form of the optimal controller solution is obtained. To solve the problem of optimal tracking for multi-agent systems with time-delay in finite time domain, a linear system with input time delay is transformed into a linear system with no time delay. According to the optimal control theory, the Riccati matrix equations are constructed, and the dynamic output feedback optimal tracking control algorithm is proposed. The correctness and validity of the conclusion are verified by computer simulation.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18;O232

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