楚天广+杨萌+李睿+张琦+张维存
摘要：本研究围绕空间合作目标的动力学分析与控制的基本目标，研究空间多关联运动体的编队控制，具有切换、非线性、异构多关联运动体分布式一致控制，逻辑动态网络中多关联运动体分析与控制，以及加权多模型自适应控制等关键问题。通过综合运用复杂系统控制理论、图论、以及非线性系统控制理论等相关知识，分析了多关联运动体的动态性质，得到了分布式协调控制的条件和设计方法。主要研究内容和结果如下。对于多关联体自驱动编队的合并与分离问题，目前文献中大多采用的方案是利用关联体之间的长程吸引和短程排斥相互作用实现系统整体的空间有界稳态分布构型。本课题通过在关联体之间引入中程排斥作用，并利用混合拓扑结构实现了系统队形的分裂和合并。关于非线性因素对多关联运动体编队控制的影响，本课题结合有向网络拓扑中非线性一阶多关联运动体的一致控制问题进行了研究，建立了控制器的设计条件。考虑到由于技术限制或外界干扰等因素，应用中通常难以实现基于全信息状态反馈的实际情况。本课题研究了未知速度量测信息和不同拓扑连接结构情形下的异构多关联运动体分布式一致控制。另外，还讨论了分布式有限时间一致性控制问题。在加权多模型自适应控制系统的分析与设计方面，进一步完善了前期的研究工作。得到了连续时间随机不确定系统的加权多模型自适应控制的稳定性条件，设计出新的加权算法并在理论上证明了其收敛性。新算法的收敛速度有明显提高，而收敛条件进一步减弱，应用范围扩大。同时，对课题前期开发的多自由度运动控制器进行了完善升级，进一步加强了系统的稳定性和实时性等方面的性能，满足了课题研究工作发展的需要。另外，研究了多关联动态逻辑系统的状态反馈镇定和最优控制问题，利用新近发展的矩阵半张量积理论，得到了全局状态反馈镇定控制器存在的代数充分必要条件，并给出了从代数表示到逻辑形式状态反馈的变换和设计步骤。对于含不确定性的概率布尔网络，得到了稳态概率分布最优控制问题可解的充分必要条件，讨论了相关的多目标优化问题并给出可行的计算方法。对于布尔网络控制系统的能观性问题，在不假设系统的能控性条件下，给出了系统能观性的充分必要条件。另外，还讨论了布尔网络的扰动解耦控制问题。以上研究结果对于理解和控制空间合作目标的复杂运动具有重要的意义。
关键词：多关联体；协调运动；编队控制；一致性协议；自适应估计；逻辑动态系统
Dynamics Analysis and Control of Coordinated Motion in Multiagent Systems
Abstract：This study is concerned with issues concerning the dynamic analysis and control of multiagent systems， including formation control of the systems， distributed consensus control of switching， non-linear， and heterogeneous systems respectively， weighted multi model adaptive control， and analysis and control of logic dynamic networks etc. based on approaches and methods from system and control theory， graph theory， and nonlinear system theory， it carries out dynamics analysis of the multiagent systems and establishes conditions of distributed coordination control and the corresponding design procedures. The main results are as follows. For the issue of formation control of self-driven multiagent systems， an approach making use of mid-range repulsive interactions and mixed topological structures is developed to realize the aggregation and splitting formation in the systems. This improves the existing methods in the literature that assume long-range attraction and short-range repulsion between a pair of agents in the systems so as to obtain bounded configurations. To study the influence of nonlinearities on collective motion of the systems， the consensus control of first-order nonlinear multiagent systems with directed network topology is considered and consensus conditions are derived， which suggest the controller design procedures. The problem of distributed control of consensus in heterogeneous multiagent systems is discussed under the assumption that only measured velocity information is available. In addition， the finite time consensus control problem is also discussed. For the issue of analysis and design of weighted multi-model adaptive control systems， the present work establishes stability conditions for continuous time systems， and gives a new algorithm for weight designed algorithm and proves its convergence. Compared with previous results， the new algorithm has a more quickly convergence speed and milder convergence conditions. The multi-degree-of-freedom motion controller that developed before is updated by enhancing the stability and real-time performance to meet the need of the project. Finally， issues of stabilization and optimal control of dynamic logic systems are investigated using the newly developed semi tensor product theory， necessary and sufficient algebraic conditions for global state feedback stabilization are obtained.
Keywords：Multiagent system； Coordinated motion； Formation control； Consensus protocol； Adaptive estimation； Dynamic logic system
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