【作者】 邓彦松；

【导师】 秦开宇；

【作者基本信息】 电子科技大学 ， 测试计量技术及仪器， 2013， 博士

【摘要】 多自主体系统整体呈现较为复杂的协调行为，而自主体之间的交互作用是局部的。当前，不论是非线性个体之间的有限时间同步还是多自主体系统的有限时间一致性，研究成果都比较少；各种队形控制方法在实际应用中精度不高且稳定性不强；路径规划算法在特定编队应用背景下容易失去全局最优解。所以多自主体编队及协调控制问题的研究具有重要的理论和现实意义。本文采用时间依赖的连续状态反馈协议，解决了多自主体系统有限时间一致性和非线性个体之间有限时间同步的问题；基于同步和一致性理论，实现了多自主体系统队形精确稳定控制；以精确稳定编队为基础，提出了基于切换拓扑和队形变换的沿墙导航人工势场算法，改善了编队路径规划算法容易陷入局部最优的缺陷。利用具有时变增益的连续状态反馈协议解决了非线性动力学系统的有限时间同步问题，得到了非线性动力学系统有限时间同步的一个充分条件。针对几类分数阶非线性动力学系统的投影同步问题，采用把分数阶非线性系统转换为等效整数阶模型，进而在这个整数阶模型上，利用Lyapunov稳定性理论，设计状态误差反馈策略实现主从系统的投影同步。多自主体系统中的个体通常呈现非线性动力学行为，因此非线性动力学系统同步问题可以认为是多自主体系统一致性的一种特例。本文在非线性动力学系统同步和有限时间同步问题的研究，不仅可为整数和分数阶非线性动力学系统的相关问题给出有效的解决方案，也为后续章节提供了理论基础和求解思路。针对多自主体系统有限时间一致性问题，本文分别对有向图和无向图进行了分析，得到了一组基于时间依赖的连续状态反馈协议的充分条件，可以使一阶和二阶多自主体系统在有限时间内达到一致性。目前已有的多自主体有限时间一致性方法大多是通过调整系统通信拓扑结构来提高Laplacian矩阵的第二最小特征值，而本文采用的方法是从协议性能出发，不需要调整系统通信拓扑结构，具有算法简单、收敛时间可以预先设定、适应面广等优点。针对不同时滞及切换拓扑结构的多自主体系统，在满足给定鲁棒性能指标的条件下，本文利用线性矩阵不等式（LMI）提出了一阶多自主体系统达到一致性的一个充分条件。噪声干扰、通信延迟和拓扑切换都是实际自主体编队和协调控制中需要面对的问题，本文提出的方法有助于分析外部干扰对多自主体系统一致性的影响，从而提高系统抗干扰能力。本文采用基于同步和一致性理论的编队图方法解决了多自主体系统队形控制的问题。以一阶和二阶多自主体系统的一致性理论保证了队形控制的稳定性，从期望的队形结构出发设计的编队图保证了队形的准确性，仅需要少量相邻个体的信息交互就可以实现整体队形的一致。用Matlab对水中机器人编队和无人机编队进行了仿真，并在水中机器人2D仿真平台和硬件平台上进行了实验验证。本文针对传统人工势场法用于编队路径规划时存在的两个明显缺陷分别提出了改进方案。提出了基于切换拓扑和队形变换的沿墙导航的改进人工势场法来防止传统人工势场法陷入局部最优；提出了利用“当前统计”模型自适应目标跟踪算法来预测机动障碍物状态，用于更新势场函数的改进方法，解决了传统人工势场法对机动目标没有跟踪预测，容易导致势场函数误差的问题。更多还原

【Abstract】 The multi-agent system behaves in comparatively complicated coordination withlocal interactions between different agents. Few study results have been achieved onfinite-time synchronization between nonlinear agents or finite-time consensus of themulti-agent system. Formation control methods lack accuracy and stability in practicalapplications. Path planning algorithms lose globally optical solutions easily in specificformation application. Therefore, the study on multi-agent formations and coordinationcontrol is of theoretical and practical significance.Using time-dependent continuous state feedback protocol, the dissertation solvesthe problem in finite-time consensus of the multi-agent system and finite-timesynchronization between non-linear agents. According to synchronization andconsensus theories, multi-agent system formations can be controlled accurately andstably. Based on accurate and stable formations, artificial potential field algorithm(APFA) for wall-following navigation built on switching topologies and formationchanges is proposed, which has overcome the shortcomings that formation pathplanning algorithm traps into local optimum easily.Finite-time synchronization of nonlinear dynamics systems are solved by use oftime-variant gain continuous state feedback, obtaining a sufficient condition for theissue. By converting the fractional-order nonlinear systems to the equivalentinteger-order models, projective synchronization of the master-slave system in differentfractional-order non-linear dynamic systems has been realized by adopt of Lyapunovstability theory and state error feedbacks. Agents in multi-agent system behave in stateof nonlinear dynamics; therefore synchronization in nonlinear dynamics systems can beregarded as a special case in the multi-agent system consensus. Studies on nonlineardynamics synchronization and finite-time synchronization in the dissertation not onlygives effective solutions to relative issues in integer-order and fractional-order nonlineardynamics systems, but also provides theoretical basis and solutions for followingsections.For finite-time consensus in the multi-agent system, after analyses on directed andundirected graphs, sufficient conditions are obtained on the basis of time-dependentcontinuous state feedback, which supports consensus of the first-order and second-ordersystems in any given limited time. Most approaches on finite-time consensus of multi-agent systems before this dissertation improve the2ndsmallest eigenvalues ofLaplacian matrix by adjusting the communication topology structure, while the methodin this dissertation concerns protocol performance without adjustment, which proves tohave simple arithmetic, convergence time presetting, generalized application and otheradvantages.For multi-agent systems in different lags and switching topology, under conditionof satisfying given H∞performance index, this dissertation proposes a sufficientcondition for first-order multi-agent system consensus by use of Linear MatrixInequality (LMI). For issues in multi-agent formation and coordinated control like noisedisturbance, communication delay and switching topology, methods presented helpsto analyze the effect of external disturbance on system consensus, thus to improve the ofdisturbance resisting capacity.The dissertation solves problems in formation control of the multi-agent system bythe formation diagram method based on synchronization and consensus theories.First-order and second-order system consensus theories ensures stability in formationcontrol, and the design for expected formation structure ensures formation accuracy,which requires information interaction between only few adjacent agents for overallformation consensus. Underwater robots formation and UAVs formation have beenstimulated by Matlab and experimental verification has been conducted in2Dsimulation platform and hardware platform for underwater robots.This dissertation proposes improvements for two obvious defects in formation pathplanning by use of traditional APFA. It presents to update APFA by wall-followingnavigation built on switching topologies and formation changes to prevent traditionalAPFA from being local optimized. An adaptive maneuvering target tracking algorithmbased on the “the current statistics” model is proposes to detect he state ofmaneuvering targets, as improvements for updating potential functions.This method hassolved lack of tracking and detecting in traditional APFA, which normally leads toerrors in potential functions.更多还原