Hierarchical-based Prescribed-time Optimal Fault-tolerant Control for Air-ground Cooperative System
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摘要: 研究了发生执行器故障的无人机−无人车异构编队系统的层级预设时间最优编队控制问题. 以保容错性能和收敛速度的优化控制为研究主线, 以层级控制、图博弈理论和预设时间控制为技术基础, 构建了一种预设时间最优容错控制算法. 虚拟层设计了基于一致性跟踪误差和能量消耗的二次型性能指标函数, 借助耦合哈密顿−雅克比−贝尔曼(Hanmilton-Jacobi-Bellman, HJB)方程和强化学习求解近似最优控制策略, 实现多智能体的同步最优控制和交互纳什均衡. 实际控制层基于最优信号并利用滑模控制和自适应技术, 设计了预设时间容错跟踪控制器, 实现对最优编队轨迹的有限时间跟踪. 在保证全局收敛时间完全不依赖于系统的初始状态和控制器参数的同时, 也有效实现对执行器故障参数的逼近. 最后, 通过仿真实验验证了所提控制策略的有效性.Abstract: This article investigates the hierarchical structure-based optimal formation control problem of a heterogeneous formation system of unmanned aerial vehicles and unmanned ground vehicles. This article focuses on the optimization control with fault-tolerant performance and fast convergence speed, and constructs a prescribed-time optimal fault-tolerant control algorithm based on hierarchical control, graphical game theory, and prescribed-time control method. In virtual layer, an quadratic performance index function based on consistency tracking error and energy consumption is designed, and approximate optimal control strategy is obtained by using coupled Hanmilton-Jacobi-Bellman (HJB) equation and reinforcement learning, which achieves synchronous optimal control and interactive Nash equilibrium of multiagent systems. In actual control layer, a prescribed-time fault-tolerant tracking controller is designed based on the optimal signal, sliding-mode and adaptive technologies, which realizes the finite-time tracking of the optimal formation trajectory. The proposed method ensures that the global convergence time is completely independent of the initial states of the system and controller parameters, while also effectively approximating the actuator fault parameters. Finally, the effectiveness of the constructed control strategy is verified through simulation experiment.
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Key words:
- Air-ground cooperation /
- actuator faults /
- prescribed-time formation /
- graphical game /
- optimal control
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图 3 虚拟层多智能体X轴一致性跟踪误差
Fig. 3 Consensus tracking errors for agents in X axis of virtual layer
图 4 虚拟层多智能体Y轴一致性跟踪误差
Fig. 4 Consensus tracking errors for agents in Y axis of virtual layer
图 5 虚拟层多智能体Z轴一致性跟踪误差
Fig. 5 Consensus tracking errors for agents in Z axis of virtual layer
图 6 实际层多智能体X轴编队跟踪误差
Fig. 6 Formation tracking errors for agents in X axis of actual layer
图 7 实际层多智能体Y轴编队跟踪误差
Fig. 7 Formation tracking errors for agents in Y axis of actual layer
图 8 实际层多智能体Z轴编队跟踪误差
Fig. 8 Formation tracking errors for agents in Z axis of actual layer
表 1 无人机和无人车的模型参数
Table 1 Model parameters of UAVs and UGVs
序号 参数 数值 1 ${\xi _{xi}},\;{\xi _{yi}},\;{\xi _{zi}}$ $1.2 \times {10^{ - 2}}\ {\rm{N}}\cdot{\rm{s}}/{\rm{rad}}$ 2 $L_i$ $0.5\ {\rm{m}}$ 3 $m_i$ $2\ {\rm{kg}}$ 4 ${\kappa _i}$ $2.98 \times {10^{ - 6}}\ {\rm{N}}\cdot{{\rm{s}}^{\rm{2}}}{\rm{/ra}}{{\rm{d}}^{\rm{2}}}$ 
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