具有随机多跳时变时延的多航天器协同编队姿态一致性

Attitude consensus of multi-spacecraft cooperative formation with stochastic multi-hop time-varying delay

针对存在随机多跳时变时延的多航天器协同编队的姿态一致性问题,本文设计了可消除随机多跳时变时延影响并能够实现多航天器协同编队姿态角速度一致及姿态角有效跟踪的静态控制器.首先基于有向图论推导出领航者一跟随者误差系统的动态方程,然后通过构造合适的Lyapunov函数将误差系统调节器问题转化为了线性矩阵不等式解的存在性问题,其次通过求解线性矩阵不等式完成了协同编队姿态控制系统的静态控制器设计.理论分析表明,所设计的控制器能够有效消除随机多跳时变时延影响,实现了多航天器协同编队的姿态一致性.数值仿真验证了所提方法的正确性和有效性.

Aiming at the attitude consensus of multi-spacecraft cooperative formation with stochastic multi-hop timevarying delay, a static controller that eliminates the influence of the time-varying delay of stochastic multi-hop time-varying delay and realizes the consensus of attitude angular velocity of multi-spacecraft cooperative formation cooperative formation as well as the effective tracking of attitude angular is designed in this paper. Firstly, based on the theory of digraph theory, dynamic equations of the leader-follower error system is deduced. Secondly, by constructing a suitable Lyapunov function, the regulator problem of the error system is transformed into the existence of the solution to the linear matrix inequalities. Finally, the static controller design of cooperative formation attitude control system is completed by solving linear matrix inequality. Theoretical analysis shows that the designed controller can effectively eliminate the effect of time-varying delay of random multi-hop and realize the attitude consensus of multi-spacecraft cooperative formation. The numerical simulation verifies the correctness and effectiveness of the proposed method.