基于齐次系统理论的多船有限时间饱和包容控制

Multiship finite-time saturation containment control based on homogeneous system theory

针对多领导者船舶编队控制问题,本文基于齐次系统有限时间稳定性理论,利用特定饱和约束函数,提出一种数学形式简化的有限时间饱和包容控制策略,实现船舶在有限时间内收敛于由虚拟领航船张成的凸包内,并保持其姿态镇定。将船舶模型化为积分形式,利用自身状态信息以及其他船舶的状态信息,提出一种饱和包容控制律;考虑闭环系统的非齐次性,综合图论知识、Lyapunov稳定性理论以及齐次系统稳定性理论等方面内容,从理论上证明编队系统中所有状态变量能够在有限时间内收敛;仿真结果证明了所提控制策略的有效性。

For the multileader ship formation control problem,this paper proposed a finite-time saturation con⁃tainment control strategy with a simplified mathematical form based on the finite-time stability theory of a homo⁃geneous system and using the specific saturation constraint function.Then,we determined whether the ship con⁃verged to the convex hull formed by the virtual leader ship in a finite time and maintained its attitude stabiliza⁃tion.First,the ship model was transformed into an integral form,after which a saturation containment control law was proposed by using its own state information and the state information of other ships.Next,we theoretically proved that all state variables in the formation system can converge in a finite time while considering the non-ho⁃mogeneity of the closed-loop system,as well as the integrated graph theory,Lyapunov stability theory and the sta⁃bility theory of homogeneous system.The simulation results demonstrated the effectiveness of the proposed con⁃trol strategy.