论文标题
一种应用于多代理最佳控制的神经网络方法
A Neural Network Approach Applied to Multi-Agent Optimal Control
论文作者
论文摘要
我们提出了一种神经网络方法，用于解决高维最佳控制问题。特别是，我们专注于具有障碍和避免碰撞的多代理控制问题。这些问题即使对于每个代理的中等空间尺寸，这些问题也会立即变得高度。我们的方法融合了Pontryagin的最大原理和Hamilton-Jacobi-Bellman（HJB）接近并通过神经网络参数化值函数。我们的方法以反馈形式产生控制，以快速计算和鲁棒性，以适度对系统的干扰。我们使用控制问题的目标函数和最佳条件来训练模型。因此，我们的培训算法既不涉及其他算法的数据生成阶段也不涉及解决方案。我们的模型使用经验有效的HJB惩罚者进行有效的培训。通过对初始状态的分布进行培训，我们确保在状态空间的很大一部分上实现控件的最优性。我们的方法无网格，并有效地缩放到网格变得不切实际或不可行的维度。我们证明了我们的方法在与障碍物的150维多代理问题上的有效性。
We propose a neural network approach for solving high-dimensional optimal control problems. In particular, we focus on multi-agent control problems with obstacle and collision avoidance. These problems immediately become high-dimensional, even for moderate phase-space dimensions per agent. Our approach fuses the Pontryagin Maximum Principle and Hamilton-Jacobi-Bellman (HJB) approaches and parameterizes the value function with a neural network. Our approach yields controls in a feedback form for quick calculation and robustness to moderate disturbances to the system. We train our model using the objective function and optimality conditions of the control problem. Therefore, our training algorithm neither involves a data generation phase nor solutions from another algorithm. Our model uses empirically effective HJB penalizers for efficient training. By training on a distribution of initial states, we ensure the controls' optimality is achieved on a large portion of the state-space. Our approach is grid-free and scales efficiently to dimensions where grids become impractical or infeasible. We demonstrate our approach's effectiveness on a 150-dimensional multi-agent problem with obstacles.
