【作者】 陈洁；

【导师】 王雅琳；

【作者基本信息】 中南大学 ， 控制理论与控制工程， 2023， 博士

【摘要】 多智能体系统包含控制作为一种多领导者协同方法,在危险品处理、救援搜查、合作运输等领域有着广泛的应用。受物理条件的限制,智能体的输入、状态(如速度、位置等)常常被约束在一定范围内。输入受限和状态约束的引入给系统建模与分析带来了困难,目前仍存在许多薄弱环节尚待解决。例如,现有受限包含控制问题的研究主要集中在输入受限,较少涉及到动态的速度和位置等状态约束;现有工作对复杂受限包含控制中时变拓扑、信息传输时滞、外部干扰等因素之间的耦合关系仍欠考虑。鉴于此,本文以状态受限的二阶离散多智能体系统为对象,考虑了速度受限、位置受限、通信拓扑时变、智能体间存在通信时滞、未知环境干扰等因素,开展了分布式包含控制的研究。论文的主要研究工作如下:(1)针对二阶离散多智能体系统不一致位置约束引起的非线性,以及非凸速度约束引起的非线性和非凸性问题,在变拓扑条件下,分析了单状态受限对系统收敛性的影响,分别设计了位置约束、速度约束下的分布式包含控制算法,给出了多智能体系统实现包含的充分条件。应用非线性投影算子描述跟随者的不一致位置约束,据此设计了基于投影的分布式包含控制算法;运用双重模型变换将非线性闭环系统转化为时变线性系统;构建了以跟随者到目标区间的最大欧氏距离为Lyapunov函数,并得到了时变拓扑条件下Lyapunov函数收敛的充分条件。对于含非凸速度约束的包含控制问题,采用约束算子描述跟随者的非凸速度约束,并设计了分布式包含控制算法;引入约束比例因子,对非线性闭环系统进行线性等价变换,巧妙解决了非凸约束难以分析的问题;给出了非凸速度约束变拓扑多智能体系统实现包含的充分条件。仿真实验证明了所提算法的有效性。(2)针对二阶离散系统中位置和速度同时受限引起的非线性耦合和非凸性等问题,考虑了不含通信时滞和含通信时滞两种情况,分别设计了分布式包含控制算法,对闭环系统模型进行三重非线性变换,并基于凸分析理论、几何分析和Lyapunov稳定性定理推导出了时变拓扑情况下闭环系统稳定的充分条件。综合考虑投影算子带来的非线性、约束算子带来的非线性和非凸性,以及速度和位置耦合对系统收敛性的影响,在时变拓扑情况下,运用比例因子和模型转换技术将非线性和非凸性的系统模型转化为线性时变模型,利用凸分析、几何分析、Lyapunov稳定性定理推导出闭环系统收敛的充分条件。进一步,考虑了智能体之间存在有界不一致通信时滞,将速度约束和位置约束的包含控制方法应用到含通信时滞的情况;设计了含非均匀时滞的Lyapunov函数,基于运动轨迹分析法,证明了速度受限、位置受限、非均匀时滞和切换有向拓扑共存时跟随者智能体的收敛性。(3)针对实际系统受到的干扰具有随机性、突发性、复杂性等特点,提出了一种带有H∞性能的分布式包含控制算法,通过提高闭环系统的鲁棒性,克服了常规基于干扰观测器控制方法的缺陷,有效抑制了干扰对位置和速度同时受限的二阶离散多智能体系统的影响。考虑到常规干扰观测器无法对随机出现的干扰进行精准估计,提出了一种H∞性能的分布式包含控制算法。通过对模型进行多次非线性变换,利用区间代数计算出系统参数的上界;设计控制输出函数估计干扰对跟随者包含误差的影响;考虑到欧氏距离的非负性,将欧氏距离函数进行放大处理,通过Lyapunov稳定性定理推导出欧氏距离能够收敛的矩阵不等式条件,给出了控制参数的计算方法。仿真实验证明,尽管存在大的干扰,所提控制方法仍然能够取得好的控制效果。(4)针对工业设备遮挡、生产环境复杂多变导致领导者难以确定可靠的目标凸区域问题,提出一种三层架构的包含控制方案,结合与实际生产场景相匹配的假设,给出变拓扑、时滞、速度和位置受限同时存在的智能无人工厂多机器人调配方案。以现代智能无人工厂多机器人调配为背景,将工业环境分散的机器人系统聚集过程看成包含控制问题,同时考虑了通信拓扑变化、时滞、速度和位置受限的情况,提出了一种三层架构的包含控制实现方案,提出的方案不需要增加机器人硬件投入,通过领导者与决策中心少量通信就能解决现有包含控制在实际应用中存在的诸多问题;设计了包含控制算法,结合与实际工业应用场景相匹配的假设条件,给出闭环系统收敛的充分条件。最后通过仿真验证了方案的有效性和可行性。图84幅,表0个,参考文献159篇更多还原

【Abstract】 Containment control of multi-agent systems is a cooperative method with multiple leaders,which has been widely used in handling of hazardous materials,searching for rescue,cooperative transportation and so on.Due to the physical limits,the control input or operation state(e.g.,the velocities and positions)of each agent is often confined in a certain range.Constraints on control input and states bring some difficulties to system modeling and analysis,and there are still many weak sections to be solved.However,the existing research on constrained-containment problems of multi-agent systems mainly focus on the saturation constraints of control input,and rarely consider the velocity and position constraints of agents.The couplings between time-varying topologies,transmission delay of information and external disturbances are not considered enough.Hence,we choose the second-order discrete-time multi-agent system with state constraints as research object,and some factors,such as velocity constraints,position constraints,the changing communication topologies,communication delays and external disturbances are considered in the studies of distributed containment control.Main work of this thesis is as follows:To solve the containment problems for second-order discrete-time multi-agent systems with nonlinearities caused by non-uniform position constraints,and nonconvexities and nonlinearities induced by nonconvex velocity constraints,the effect of single-state constraint on the convergence of system is analyzed.Two kinds of distributed containment algorithms are designed for multi-agent system with position and velocity constraints,respectively.Corresponding sufficient conditions for the achievement of containment are given.Firstly,a nonlinear projection operator is used to describe the non-uniform position constraints of each follower,and a projection-based distributed containment algorithm is designed.The nonlinear closed-loop system is transformed into a time-varying linear system by double model transformations.By choosing the largest Euclidean distance from all followers to the target area as the Lyapunov function,and the sufficient condition for the convergence of the Lyapunov function is obtained.The containment control problem with nonconvex velocity constraints is investigated,and a constraint operator is introduced to describe the nonconvex velocity constraints of each follower.Then,a distributed containment control algorithm is designed,and the difficulties existing in the analyzing the containment problem with nonconvex constraints is neatly solved by introducing the scale factors and using model equivalent transformations.The sufficient condition for achieving the containment with nonconvex velocity constraints is derived.Some simulation experiments are performed to illustrate the effectiveness of the proposed algorithms.Given that the coexistence of nonlinearites and nonconvexites caused by the convex position and nonconvex velocity constraints in multi-agent systems,the distributed containment control algorithms are designed for the containment problems with or without considering communication delays,respectively,and corresponding sufficient conditions for the achievement of those two containments are derived by triple model nonlinear transformations,convex analysis and the Lyapunov stability theorem.By considering the effect of the nonlinearities caused by the projection and constraint operators,nonconvexities induced by constraint operator,the coupling between velocity and position,we convert the nonlinear and nonconvex model into a linear time-varying model via scale factor and model transformation technique.The convex analysis,geometrical analysis and the Lyapunov stability theorem are used to prove the convergence of the closed-loop system.Furthermore,we extend the containment control method to the situation with bounded non-uniform communication delays,and design the Lyapunov function with communication delays.Based on the root locus method,it is proved the convergence of followers with the coexistence of the non-uniform communication delays,directed switching topologies,convex position and nonconvex velocity constraints.Due to the random,abruptness and complexity of actual disturbances,a distributed containment control algorithm with H∞ performance is proposed to improve the robustness of the closed-loop system.The proposed method can overcome the shortcomings of the observer-based containment control method,and reject the effect of the disturbance on the multi-agent system with position and velocity constraints.Because general disturbance observers can not estimate the disturbance accurately,a distributed containment control algorithm with H∞ performance is designed.The closed-loop system model is converted to a time-varying linear system by multiple nonlinear transformations,and interval computation is adopted to calculate the upper bound of each system parameter.A nonlinear output function is constructed to measure the effect of disturbance on the convergence of each follower.Given the non-negative of the Euclidean distance function,we enlarge the Euclidean distance function,and give the convergence condition of the Euclidean distance function in terms of matrix inequality.The computation method of control parameters is provided.The results of some simulation experiments show that the proposed method can still achieve good control performance for large disturbances.Considering the communication interrupt caused by industrial equipment shielding,and the unreliable target area determined by the detected information around leaders,a three-layer containment control framework is proposed.Combined with the hypothesis matching the actual production scene,a deployment scheme is presented to solve the deployment of multiple robots in complex and changeable production environment,where time-varying topologies,time delay,speed and position constraints are considered.Taking the deployment of multiple robots in modern intelligent unmanned factory as the background,gathering problem of the scattered robots in industrial environment can be viewed as a containment control problem.By taking the changing of the communication topologies,communication delays,position and velocity constraints into consideration,a containment control scheme with three-layer framework is proposed.Note that proposed scheme need not add the cost of hardware on robot,and some drawbacks of the general containment control method can be overcome via a small amount of communication between the leader and the decision center.Combining with the assumption matching the actual production scene,a control method for such problem is constructed,and a sufficient condition for the convergence of each robot is given,and the effectiveness and feasibility of this control scheme are verified by some simulation.更多还原