Adaptive Dynamic Event-Triggered Optimal Control for Vehicle Platoon System under Jointly Connected Switching Topology
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摘要: 针对通信带宽有限且存在输入饱和的非线性多车队列系统, 本文研究联合切换拓扑与通信延迟下模糊自适应动态事件触发最优控制设计问题. 首先, 为具有输入饱和的队列系统构建新的性能指标函数. 其次, 采用积分强化学习方法在线求解最优控制中的哈密顿-雅可比-贝尔曼方程, 并针对积分强化学习中对于持续激励条件的严格要求, 提出基于经验回放机制的梯度下降以更新模糊逻辑系统权重, 进而放宽传统积分强化学习对持续激励条件的严格要求. 在此基础上, 本文分别在通信端与控制端引入双重动态事件触发机制, 有效节省车载资源. 通过构造李雅普诺夫函数并结合平均驻留时间方法, 证明闭环系统中所有信号最终一致有界. 与现有的事件触发机制相比, 所提出双重事件触发机制可节省60.81%资源. 数值仿真结果进一步验证上述所提出动态事件触发最优控制方法的有效性.Abstract: For nonlinear vehicle platoon systems with limited communication bandwidth and input saturation, this paper investigates the issue of fuzzy adaptive dynamic event-triggered optimal control under jointly switching topologies and communication delays. Firstly, a novel performance index function is constructed for the platoon system with input saturation. Furthermore, an integral reinforcement learning method is employed to online solve the Hamilton-Jacobi-Bellman equation in the optimal control. To address the strict requirement of the persistence of excitation condition in integral reinforcement learning, a gradient descent method based on an experience replay mechanism is proposed to update the weights of the fuzzy logic system, thereby relaxing the strict persistence of excitation condition required by traditional integral reinforcement learning. On this basis, a dual dynamic event-triggered mechanism is introduced at both the communication and control ends which can effectively save on-board resources. By constructing a Lyapunov function and employing the average dwell time method, it is proven that all signals in the closed-loop system are uniformly ultimately bounded. Compared with the existing event triggered mechanisms, the proposed dual event-triggered mechanism saves 60.81% resources. Numerical simulation results further verify the effectiveness of the developed dynamic event-triggered optimal control method.
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表 1 跟随车的参数
Table 1 The parameters of the followers
车辆$ i $ 跟随车1 跟随车2 跟随车3 跟随车4 $ l_i({\rm{m}}) $ 2.3 3.4 2.4 3.2 $ A_i({\rm{m}}^2) $ 0.21 0.3 0.25 0.27 $ m_i({\rm{kg}}) $ 1100 1050 1200 1300 $ r_i $ 0.01 0.02 0.015 0.02 $ \tau_i $ 0.4 0.3 0.4 0.45 
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表 2 队列系统的初始状态
Table 2 Initial status of the platoon system
车辆$ i $ $ p_i(0)({\rm{m}}) $ $ v_i(0)({\rm{m/s}}) $ $ a_i(0)({\rm{m/s}}^2) $ 领航车0 22 15 0 跟随车1 16.5 14.5 0 跟随车2 11.2 14 0 跟随车3 6.1 13.5 0 跟随车4 0.8 13 0
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表 3 部分仿真参数
Table 3 Partial simulation parameters
参数 值 参数 值 $ Q_i $ 1 $ {\rm{P}}_i $ 0.9 $ R_{ii} $ 1 $ \alpha_{i,\;1} $ 1 $ R_{ij} $ 1 $ \alpha_{i,\;2} $ 8 $ \alpha_i^c $ 1.4 $ \alpha_{i,\;3} $ 0.1 $ \lambda_{i,\;2}(0) $ 5 $ \alpha_{i,\;4} $ 0.3 $ \Phi_i $ 0.4 $ \alpha_{i,\;5} $ 2 $ \varphi_i $ 5 $ \alpha_{i,\;6} $ 0.02 $ \omega_i $ 0.9 $ \bar{\varepsilon} $ 0.001
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