基于Helly定理的多智能体最短时间一致性

多智能体一致性协调控制的最终收敛状态受限于通信拓扑结构与边的权值,而收敛状态的不同进一步影响多智能体趋同的速度.为实现拓扑结构与协调收敛状态解耦,保证最短时间实现一致性,本文设计一种输入受限线性多智能体分布式协调控制策略.首先基于Helly定理证明了n个输入受限线性多智能体系统在d(nd)维协调空间上的最短时间一致性协调状态和收敛时间唯一存在,并取决于其中至多d+1个智能体.当找到该d+1个起决定作用的智能体后,即可得到所有智能体的最短时间一致性状态.根据此定理,设计一种新的分布式协调算法使得各个智能体知道起决定作用的智能体,进而计算得到协调收敛状态与收敛时间,随后各个智能体独立设计含终端时间和终端状态约束的局部最优控制律,保证最短时间一致性实现.最后在二阶线性多智能体系统上进行仿真验证.仿真结果验证了分布式算法的可行性,并且当协调状态维度远小于智能体数量时,计算量明显减少,计算速度显著增加.

Helly-theorem-based time-optimal consensus for multi-agent systems

The final convergence state of multi-agent under ordinary consensus control is restricted by communication topology structure and edge weight. Different convergence states further influence the convergence speed of multi-agent. To attain identical convergence state under different communication topologies, and achieve time-optimal consensus, we designed a time-optimal distributed consensus control strategy for linear multi-agent system with input constraint. Firstly, we proved that the time-optimal consensus state and convergence time uniquely existed based on Helly theorem. More specifically, for the multi-agent system with n agents with input constraint in the d(n >d) dimension state space, the time-optimal state can be determined by d+1 agents at most. When the d+1 crucial agents were obtained, so was the consensus state. According to this theorem, we designed a new distributed coordination algorithm for multi-agent to achieve common knowledge on those critical agents together with the time-optimal consensus state and convergence time, and after that, each of the agents designed its own local optimal control law with terminal-time and terminal-state constraints, which guaranteed the time-optimal consensus of multi-agent. To demonstrate the correctness and efficiency of the algorithm, we applied our algorithm to the second-order dynamic multi-agent systems. Simulation result verifies the feasibility of the distributed algorithm. When the coordinating state dimension is much smaller than the number of agents, the algorithm significantly reduces the amount of computations and increases computation speed.