基于领航者跟随者的群系统保性能编队控制

王琳; 张庆杰; 陈宏伟

doi:10.13700/j.bh.1001-5965.2022.0371

基于领航者跟随者的群系统保性能编队控制

doi: 10.13700/j.bh.1001-5965.2022.0371

空军航空大学，长春 130022

详细信息

通讯作者:
E-mail：nudtzhang@hotmail.com

中图分类号: V249
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- 被引次数: 0
出版历程
- 收稿日期: 2022-05-17
- 录用日期: 2023-02-24
- 网络出版日期: 2023-09-04
- 整期出版日期: 2024-03-27

Guaranteed-performance formation control of swarm systems based on leader-follower strategy

Aviation University of Air Force，Changchun 130022，China

More Information

Corresponding author: E-mail：nudtzhang@hotmail.com

摘要

摘要:
针对群系统编队跟踪控制问题，提出了一种切换拓扑下保性能的优化控制方法。建立了基于领航跟随结构的编队跟踪控制问题的数学描述，引入分布式性能指标描述群系统编队调节性能。利用一致性理论设计了基于领航跟随结构的编队控制协议。借助李雅普诺夫方法分析系统的闭环稳定性，给出保性能上界的数学表达形式。利用数值仿真验证了所提控制方法的有效性，群系统可在性能上界下实现编队跟踪控制，且在编队跟踪速度和消耗性能方面优于已有文献。
- 群系统 /
- 领航跟随 /
- 编队跟踪 /
- 保性能 /
- 切换拓扑
Abstract:
Aiming at the problem of formation tracking control of swarm systems, an optimal control method with guaranteed-performance with switching topologies is proposed. Firstly, a mathematical description of formation tracking control problem based on leader-follower structure is established, and a distributed performance index is introduced to describe the formation adjustment performance of swarm systems. Then, the formation control protocol based on leader-follower structure is designed by using consensus theory. Then, the closed-loop stability of the system is analyzed by means of Lyapunov method, and the mathematical expression of the upper bound of the guaranteed-performance is given. Finally, a numerical simulation is used to verify the effectiveness of the control method, and the swarm system can realize formation tracking control under the upper bound of performance, and the formation tracking speed and performance consumption are better than the existing literature.
- swarm systems /
- leader-follower /
- formation tracking /
- guaranteed-performance /
- switching topology

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图 1 领航者跟随者之间的拓扑图

Figure 1. Topologies between leader and followers

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图 2 跟随者的三维运动轨迹

Figure 2. Three-dimensional trajectories of followers

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图 3 跟随者的轨迹侧视图

Figure 3. Lateral view of trajectories of followers

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图 4 不同时刻主体状态演化过程

Figure 4. State evolution process of agents at different times

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图 5 3个不同方向上的领航者跟踪误差

Figure 5. Leader tracking errors in three different directions

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图 6 3个不同方向上的编队跟踪误差

Figure 6. Formation tracking errors in three different directions

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图 7 实际消耗性能指标与性能上界

Figure 7. Actual consumed performance index and upper bound of guaranteed performance

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图 8 不同方法下消耗性能指标

Figure 8. Cost of performance index in different methods

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表 1 编队跟踪误差收敛时间

Table 1. Convergence time of formation tracking errors

$ \alpha $	收敛时间/s
0.2	4.8
0.4	4.7
0.6	4.6
0.8	4.2
1.0	4.1

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表 2 不同方法下编队跟踪误差收敛时间、消耗性能指标和控制参数取值

Table 2. Convergence time of formation tracking errors, cost of performance and values of control parameters in different methods

方法	收敛时间/s	消耗性能指标	控制参数取值
本文方法	9.6	742.1088	$ \begin{gathered} {{\boldsymbol{K}}_1} = \left[ {\begin{array}{{20}{r}} { - 2.938\;9}&{ - 2.979\;9}&{ - 0.791\;3}&{0.074\;8}&{0.863\;8}&{0.389\;0} \\ {0.985\;1}&{ - 0.007\;6}&{ - 2.891\;5}&{ - 2.987\;5}&{0.462\;8}&{0.221\;8} \\ { - 0.324\;9}&{ - 0.119\;7}&{0.009\;4}&{ - 0.179\;9}&{ - 2.083\;4}&{ - 3.032\;6} \end{array}} \right] \\ {{\boldsymbol{K}}_2} = {{\boldsymbol{I}}_3} \otimes \left[ {\begin{array}{{20}{c}} {30.011\;2}&{29.798\;4} \end{array}} \right] \\ \end{gathered} $
文献[26,37]	12.1	797.3386	$ {{\boldsymbol{K}}}_{1}={{\boldsymbol{I}}}_{3}\otimes \left[\begin{array}{cc}-8.560\;4& -11.757\;4\end{array}\right]，{{\boldsymbol{K}}}_{2}={{\boldsymbol{I}}}_{3}\otimes \left[\begin{array}{cc}8.560\;4& 11.757\;4\end{array}\right] $
文献[27,38-39]	15.3	877.5561	$ {{\boldsymbol{K}}}_{1}={{\boldsymbol{I}}}_{3}\otimes \left[\begin{array}{cc}-5.364\;8& -9.292\;1\end{array}\right]，{{\boldsymbol{K}}}_{2}={{\boldsymbol{I}}}_{3}\otimes \left[\begin{array}{cc}5.364\;8& 9.292\;1\end{array}\right] $
文献[28]	11.9		$ {{\boldsymbol{K}}}_{1}={{\boldsymbol{I}}}_{3}\otimes \left[\begin{array}{cc}-3.170\;5& -4.354\;6\end{array}\right]，{{\boldsymbol{K}}}_{2}={{\boldsymbol{I}}}_{3}\otimes \left[\begin{array}{cc}3.170\;5& 4.354\;6\end{array}\right] $

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