具有时滞的线性多自主体系统趋同控制研究

发布时间：2018-05-06 17:58

本文选题：多自主体系统 + 通信时滞　；参考：《山东大学》2017年博士论文

【摘要】：近年来,随着控制理论、计算机技术、网络信号处理和通信技术的不断发展,网络多自主体系统的趋同控制问题受到了国内外广大学者的关注,也出现了许多有价值的研究成果.本文在已有的工作基础上,研究了几类具有定常通信时滞和带约束的线性多自主体系统的趋同控制问题,取得如下的研究成果:1.考虑在无向通信网络中,一般连续时间线性多自主体系统的趋同控制问题.状态矩阵和输入矩阵的一般性和时滞的存在给趋同性问题的研究带来困难.通过引入适当的线性变换,我们将趋同性问题转化为等价的与拉普拉斯矩阵的特征根相关的多个时滞子系统的同步镇定性问题,从而建立了趋同性问题和稳定性问题之间的联系.我们利用线性矩阵不等式方法和李雅普诺夫稳定性理论,得到了保证多个时滞子系统同步镇定的充分条件.对于每个自主体都是一阶积分器系统的情况,我们直接使用频域分析方法得到了保证趋同的显式条件.我们也找到了一个时滞界与参数的关系,从而不管时滞大小,只要拉普拉斯矩阵的特征根满足某个特定的关系,多自主体系统总是可以达到趋同的.2.考虑一类一般形式的二阶线性多自主体动态模型的趋同问题,同时涉及到通信延迟.我们希望能找到保证系统达到二阶趋同的最大容许时滞界,对此我们的处理方法是:首先,我们考虑无时滞控制协议,通过引入适当的线性变换,将可趋同性问题转化为等价的镇定性问题.通过分析闭环系统的特征多项式的稳定性得到无时滞情形下多自主体系统达到趋同的充分必要条件.特别地,对于二阶积分器系统可以对应地得到相应的趋同条件.然后,在假设无时滞趋同条件成立的基础上,我们考虑具有定常通信时滞的控制协议,通过分析闭环系统特征方程的根和时滞参数的关系,得到了保证趋同的时滞界的显式表达式.这使得我们意识到在趋同的收敛性质和时滞大小之间有一个折中关系.针对特殊系统,即二阶积分器系统,我们给出更详细的分析,而且给出时滞界的更简单的显式表达式.3.在无向连通网络中,考虑一类一般形式的三阶线性动态模型的趋同问题.考虑三阶系统趋同问题的意义在于,首先三阶系统可以模拟实际生活中的一类物理系统,比如车辆的纵向动力学模型;其次趋同问题可以表征多个物理系统共同呈现的某种群体行为.本章的贡献之一在于通过分析闭环系统特征方程根的分布情况,给出了此类一般三阶系统达到无时滞趋同的充分必要条件.第二个贡献在于对于三阶积分器系统,在假设无时滞情形下达到趋同的条件成立的基础上,提供了一种计算系统趋同可容许通信时滞的方法.4.考虑具有时滞的离散时间多自主体系统的带约束趋同问题.首先,给出了无时滞无约束趋同的充分必要条件.然后,考虑无时滞带约束的趋同问题,将闭环系统分解成两个部分,我们会发现保证趋同的要求比无时滞无约束的情况的要求高.继而基于无时滞无约束情形下的趋同条件,考虑具有时滞的无约束趋同问题,得到了达到趋同的充分必要条件.这个条件是指数方程的形式,而且我们只对无向图时滞为1或2的情形给出了显式形式的保证趋同的充分必要条件.最后,我们考虑具有时滞的带约束的趋同问题,可以发现确保无时滞带约束情形的趋同条件也可以保证具有时滞的带约束问题达到趋同.
[Abstract]:In recent years, with the continuous development of control theory, computer technology, network signal processing and communication technology, the convergence control problem of network multi agent system has been paid attention by many scholars at home and abroad, and many valuable research results have appeared. On the basis of existing work, several kinds of time-delay and time-delay are studied. The following research results are obtained as follows: 1. consideration is given to the convergence control problem of a general continuous time linear multi-agent system in an undirected communication network. The existence of the generality and delay of the state matrix and the input matrix brings difficulties to the study of the convergence problem. In the linear transformation, we transform the homosexual problem into an equivalent synchronous town qualitative problem of multiple time-delay subsystems associated with the eigenvalues of the Laplasse matrix, thus establishing the connection between the homosexual problem and the stability problem. We get the guarantee by using the linear matrix inequality method and Lyapunov stability theory. A sufficient condition for simultaneous stabilization of multiple time-delay subsystems. For every self agent is a first order integrator system, we use the frequency domain analysis method to obtain the explicit condition of convergence. We also find a relationship between the time delay bound and the parameter, so that the eigenvalue of the Laplasse matrix is satisfied regardless of the time delay. A particular relationship, the multiple self body system can always reach the convergent.2., consider the convergence problem of a class of two order linear multiple self agent dynamic models in general form, and involve the communication delay. We hope to find the maximum admissible time delay bound for the two order convergence of the guaranteed system. Considering the non delay control protocol, by introducing the appropriate linear transformation, the homosexual problem can be transformed into an equivalent qualitative problem. By analyzing the stability of the characteristic polynomial of the closed loop system, the sufficient and necessary conditions for the convergence of the multi agent system in the case of no delay are obtained. In particular, the two order integrator system can correspond to the condition. The corresponding convergence conditions are obtained. Then, on the basis of the assumption that the time delay convergence condition is established, we consider the control protocol with constant communication delay. By analyzing the relationship between the root and time delay parameters of the characteristic equation of the closed loop system, we get the explicit expression of the time delay bound to guarantee the convergence. There is a tradeoff between the nature and the time delay size. For the special system, that is, the two order integrator system, we give more detailed analysis, and give a more simple explicit expression.3. in the time delay boundary. In the undirected connected network, we consider the convergence problem of a class of three order linear dynamic model of the general form. Consider the convergence of the three order system. The significance of the problem is that the first three order system can simulate a class of physical systems in real life, such as the longitudinal dynamic model of a vehicle, and then the convergence problem can represent a certain group behavior that multiple physical systems present together. One of the contributions of this chapter is to analyze the distribution of the root of the characteristic equation of the closed loop system. The general three order system has sufficient and necessary conditions for the convergence without delay. The second contribution is to provide a method for calculating the convergence of the time delay for the convergence of the three order integrator system, on the basis of the assumption that there is no delay in the condition of convergence..4. considers the discrete time multi agent system with time delay. First, we give the sufficient and necessary conditions for the convergence without delay and unconstrained convergence. Then, considering the convergence problem with no delay band constraints, the closed loop system is decomposed into two parts. We will find that the requirement for the convergence is higher than that without delay and unconstrained conditions. Then, the convergence is based on the convergence without delay and unconstrained conditions. Conditions, considering the unconstrained convergence problem with time delay, we get the sufficient and necessary condition for reaching the convergence. This condition is the form of the exponential equation, and we give the sufficient and necessary conditions for the explicit form to guarantee the convergence of the explicit form in the case of the undirected graph with 1 or 2. Finally, we consider the convergence problem with time delay with constraint. It can be found that convergence conditions with guaranteed delay without delay can guarantee convergence of the constrained problem with time delay.

【学位授予单位】：山东大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP13

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