多智能体的一致性控制及优化
发布时间：2019-06-08 11:53
【摘要】：近年来,多智能体系统由于在诸如微电网能量管理与优化、微电网需求响应管理,无线传感器网络故障诊断与拥塞控制、无人驾驶飞行器姿态调节、无人车驾驶等诸多工程领域中的应用而得到了广泛的关注。其中,多智能体系统的一致性是实现工程应用的理论基础。本论文主要致力于探讨多智能体系统的一致性控制及其在求解凸优化问题中的应用,其主要工作分为以下几个方面:1主要介绍多智能体系统的研究背景与研究意义以及本论文所做的工作。2探讨了基于均匀采样控制的二阶多智能体系统的领航-跟随一致性问题。通过设计包含实时位置和速度信息以及采样位置和速度信息的控制器,运用代数图论和线性系统理论,分析受控系统的特征多项式,得到了使二阶系统达到一致的充分必要条件。获得的结论表明:受控二阶多智能体系统能够达到一致当且仅当采样周期和耦合增益满足一些代数不等式条件。最后,通过两个仿真的例子阐明了本章中理论分析的有效性。3探讨了基于事件的广义线性多智能体系统的半全局领航-跟随一致性控制问题。与2中探讨的均匀采样方式不同的是,本章中采样控制器的采样间隔是由一组“事件”决定的,其采样周期一般不均匀。本章考虑的模型是带有输入饱和的多智能体系统。半全局一致性指的是多智能体系统达到一致性与否与系统初始值的选取相关。通过运用代数图论、M矩阵理论和Lyapunov方法,设计了两类基于事件的采样控制器:基于连续时间信息交换的事件触发采样控制器、基于离散时间信息交换的自触发采样控制器。在假设领航节点全局可达的前提下,分别针对这两类控制器,获得了使受控多智能体系统达到领航-跟随一致的代数不等式形式的判据。此外,对于这两类控制器,还分别证明了它们相邻两个触发时刻的间隔是有下界的,即Zeno效应不会发生。最后通过两个仿真例子阐明了本章中理论分析的有效性与正确性。4探讨了基于异步通讯的离散时间多智能体系统的约束一致问题。所谓约束一致性,是指在多智能体系统中,每一个智能个体的状态均只能在一个凸约束集内选取。与2、3中的研究不同的是,本章在多智能体系统中引入了投影算子以体现状态约束的存在。值得指出的是,在多智能体系统中引入状态约束的同时,也在系统中引入了非线性性。为了处理异步通讯带来的信息处理不同步的问题,作者提出了一类在网络中添加“非计算”智能体的方法,以此将异步通讯系统等价转化为同步通讯系统。针对转化后的同步通讯系统,为了处理由投影算子引入的非线性性,多智能体系统被分为线性部分和非线性部分进行研究,运用凸集上投影的性质以及添加节点后系统方程的状态转移矩阵的性质,证明了多智能体系统方程的线性部分收敛,同时其非线性部分趋近于零,继而证明了一致性。最后通过两个仿真例子阐明了本章中异步通讯算法的有效性与正确性。5探讨了带有不等式约束以及随机投影的多智能体凸优化问题。凸优化问题的目标函数是由多个子目标函数相加而成,这些子目标函数均为凸函数,其约束条件为全局不等式约束以及随机出现的状态凸约束集,为了求解此问题,构造了基于多智能体系统的分布式原-对偶随机投影次梯度算法,该算法分为两个部分:信息融合部分以及次梯度下降部分。在信息融合部分中,智能体将自身信息与从邻节点接收的信息以加权平均的方式进行融合;在次梯度下降部分中,智能体选择局部拉格朗日函数的次梯度反方向作为下降方向,并结合搜索步长计算得到状态更新,对于上述多智能体优化算法,运用适当的迭代不等式和凸优化理论,证明了其在二次收敛步长下的收敛性,即多智能体优化算法最终收敛于优化问题的最优解。最后,通过一个数值例子阐明了本章中理论分析的有效性与正确性。
[Abstract]:in recent year, that multi-agent system is adapt to the attitude of the unmanned aerial vehicle due to the management and optimization of the energy management and optimization of the micro-grid, the demand response management of the micro-grid, the fault diagnosis and congestion control of the wireless sensor network, the attitude adjustment of the unmanned aerial vehicle, The application of unmanned vehicle driving and other engineering fields has received wide attention. The consistency of multi-agent system is the theoretical basis for the application of engineering. This paper is devoted to discussing the consistency control of multi-agent system and its application in solving the problem of convex optimization. The main work is divided into the following aspects:1. The research background and research significance of the multi-agent system and the work done in this paper are mainly introduced. The pilot-following consistency of the second-order multi-agent system based on the uniform sampling control is discussed. By designing the controller which contains the real-time position and velocity information and the sampling position and velocity information, the characteristic polynomial of the controlled system is analyzed by using the algebraic graph theory and the linear system theory, and a sufficient and necessary condition for the second-order system to reach the agreement is obtained. The obtained conclusions show that the controlled second-order multi-agent system can be consistent and only when the sampling period and the coupling gain satisfy some algebraic inequality conditions. Finally, the validity of the theory analysis in this chapter is illustrated by two examples, and the semi-global pilot-following consistency control problem of the generalized linear multi-agent system based on the event is discussed. The sampling interval of the sampling controller in this chapter is determined by a set of "event", and its sampling period is generally not uniform. The model considered in this chapter is a multi-agent system with input saturation. The semi-global consistency refers to the correlation between the consistency of the multi-agent system and the selection of the initial value of the system. By using the algebraic graph theory, the M-matrix theory and the Lyapunov method, two kinds of event-based sampling controllers are designed: the event trigger sampling controller based on the continuous time information exchange, the self-triggering sampling controller based on the discrete time information exchange. On the premise that the global reach of the pilot node is assumed, the criterion of making the controlled multi-agent system reach the form of a pilot-follow-consistent algebraic inequality is obtained for both types of controllers. In addition, for both types of controllers, it is also proved that the interval between the two adjacent trigger moments is a lower bound, that is, the Zeno effect does not occur. In the end, the validity and validity of the theory analysis in this chapter are illustrated by two simulation examples. The so-called constraint consistency means that in a multi-agent system, the state of each of the smart individuals can only be selected within a set of convex constraints. It is different from the research in 2 and 3. In this chapter, the projection operator is introduced in the multi-agent system to reflect the existence of the state constraint. It is worth noting that the introduction of a state constraint in a multi-agent system also introduces non-linearity in the system. In order to solve the problem of the non-synchronization of information processing brought by asynchronous communication, the author puts forward a class of method to add the "non-calculation" agent in the network, so as to convert the equivalent of the asynchronous communication system into the synchronous communication system. In order to deal with the non-linearity introduced by the projection operator, the multi-agent system is divided into a linear part and a non-linear part for studying the non-linearity introduced by the projection operator, The convergence of the linear part of the multi-agent system equation is proved, and the non-linear part of the system is close to zero, and then the consistency is proved. Finally, the validity and correctness of the asynchronous communication algorithm in this chapter are illustrated by two simulation examples. the objective function of the convex optimization problem is obtained by adding a plurality of sub-objective functions, each of the sub-objective functions is a convex function, the constraint condition is a global inequality constraint and a randomly-occurring state convex constraint set, and in order to solve the problem, A distributed primary-dual random projection subgradient algorithm based on a multi-agent system is constructed. The algorithm is divided into two parts: an information fusion part and a sub-gradient descending part. in the information fusion part, the intelligent body integrates the self information with the information received from the adjacent node in a weighted average way; in the sub-gradient descent part, the intelligent body selects the sub-gradient reverse direction of the local Lagrange function as the descending direction, And the convergence of the multi-agent optimization algorithm under the second convergence step is proved by using an appropriate iterative inequality and a convex optimization theory in combination with the search step size calculation, that is, the multi-agent optimization algorithm finally converges to the optimal solution of the optimization problem. Finally, the validity and correctness of the theory analysis in this chapter are illustrated by a numerical example.
【学位授予单位】：西南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP18;TP13
本文编号：2495264
[Abstract]:in recent year, that multi-agent system is adapt to the attitude of the unmanned aerial vehicle due to the management and optimization of the energy management and optimization of the micro-grid, the demand response management of the micro-grid, the fault diagnosis and congestion control of the wireless sensor network, the attitude adjustment of the unmanned aerial vehicle, The application of unmanned vehicle driving and other engineering fields has received wide attention. The consistency of multi-agent system is the theoretical basis for the application of engineering. This paper is devoted to discussing the consistency control of multi-agent system and its application in solving the problem of convex optimization. The main work is divided into the following aspects:1. The research background and research significance of the multi-agent system and the work done in this paper are mainly introduced. The pilot-following consistency of the second-order multi-agent system based on the uniform sampling control is discussed. By designing the controller which contains the real-time position and velocity information and the sampling position and velocity information, the characteristic polynomial of the controlled system is analyzed by using the algebraic graph theory and the linear system theory, and a sufficient and necessary condition for the second-order system to reach the agreement is obtained. The obtained conclusions show that the controlled second-order multi-agent system can be consistent and only when the sampling period and the coupling gain satisfy some algebraic inequality conditions. Finally, the validity of the theory analysis in this chapter is illustrated by two examples, and the semi-global pilot-following consistency control problem of the generalized linear multi-agent system based on the event is discussed. The sampling interval of the sampling controller in this chapter is determined by a set of "event", and its sampling period is generally not uniform. The model considered in this chapter is a multi-agent system with input saturation. The semi-global consistency refers to the correlation between the consistency of the multi-agent system and the selection of the initial value of the system. By using the algebraic graph theory, the M-matrix theory and the Lyapunov method, two kinds of event-based sampling controllers are designed: the event trigger sampling controller based on the continuous time information exchange, the self-triggering sampling controller based on the discrete time information exchange. On the premise that the global reach of the pilot node is assumed, the criterion of making the controlled multi-agent system reach the form of a pilot-follow-consistent algebraic inequality is obtained for both types of controllers. In addition, for both types of controllers, it is also proved that the interval between the two adjacent trigger moments is a lower bound, that is, the Zeno effect does not occur. In the end, the validity and validity of the theory analysis in this chapter are illustrated by two simulation examples. The so-called constraint consistency means that in a multi-agent system, the state of each of the smart individuals can only be selected within a set of convex constraints. It is different from the research in 2 and 3. In this chapter, the projection operator is introduced in the multi-agent system to reflect the existence of the state constraint. It is worth noting that the introduction of a state constraint in a multi-agent system also introduces non-linearity in the system. In order to solve the problem of the non-synchronization of information processing brought by asynchronous communication, the author puts forward a class of method to add the "non-calculation" agent in the network, so as to convert the equivalent of the asynchronous communication system into the synchronous communication system. In order to deal with the non-linearity introduced by the projection operator, the multi-agent system is divided into a linear part and a non-linear part for studying the non-linearity introduced by the projection operator, The convergence of the linear part of the multi-agent system equation is proved, and the non-linear part of the system is close to zero, and then the consistency is proved. Finally, the validity and correctness of the asynchronous communication algorithm in this chapter are illustrated by two simulation examples. the objective function of the convex optimization problem is obtained by adding a plurality of sub-objective functions, each of the sub-objective functions is a convex function, the constraint condition is a global inequality constraint and a randomly-occurring state convex constraint set, and in order to solve the problem, A distributed primary-dual random projection subgradient algorithm based on a multi-agent system is constructed. The algorithm is divided into two parts: an information fusion part and a sub-gradient descending part. in the information fusion part, the intelligent body integrates the self information with the information received from the adjacent node in a weighted average way; in the sub-gradient descent part, the intelligent body selects the sub-gradient reverse direction of the local Lagrange function as the descending direction, And the convergence of the multi-agent optimization algorithm under the second convergence step is proved by using an appropriate iterative inequality and a convex optimization theory in combination with the search step size calculation, that is, the multi-agent optimization algorithm finally converges to the optimal solution of the optimization problem. Finally, the validity and correctness of the theory analysis in this chapter are illustrated by a numerical example.
【学位授予单位】：西南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP18;TP13
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2 刘金琨,尔联洁;多智能体技术应用综述[J];控制与决策;2001年02期
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