Safe control of neural network dynamic models (NNDMs) is important to robotics and many applications. However, it remains challenging to compute an optimal safe control in real time for NNDM. To enable real-time computation, we propose to use a sound approximation of the NNDM in the control synthesis. In particular, we propose Bernstein over-approximated neural dynamics (BOND) based on the Bernstein polynomial over-approximation (BPO) of ReLU activation functions in NNDM. To mitigate the errors introduced by the approximation and to ensure persistent feasibility of the safe control problems, we synthesize a worst-case safety index using the most unsafe approximated state within the BPO relaxation of NNDM offline. For the online real-time optimization, we formulate the first-order Taylor approximation of the nonlinear worst-case safety constraint as an additional linear layer of NNDM with the l2 bounded bias term for the higher-order remainder. Comprehensive experiments with different neural dynamics and safety constraints show that with safety guaranteed, our NNDMs with sound approximation are 10-100 times faster than the safe control baseline that uses mixed integer programming (MIP), validating the effectiveness of the worst-case safety index and scalability of the proposed BOND in real-time large-scale settings. The code is available at https://github.com/intelligent-control-lab/BOND.

翻译：神经网络动力学模型的安全控制对于机器人及众多应用领域至关重要。然而，实时计算神经网络动力学模型的最优安全控制仍具挑战。为实现实时计算，我们提出在控制综合中采用可靠近似策略。具体而言，基于伯恩斯坦多项式对神经网络动力学模型中ReLU激活函数的过近似，提出伯恩斯坦过近似神经网络动力学（BOND）方法。为缓解近似引入的误差并确保安全控制问题的持续可行性，我们离线利用神经网络动力学模型的BPO松弛中最不安全近似状态，合成最坏情况安全指标。在线实时优化中，我们将非线性最坏情况安全约束的一阶泰勒近似建模为神经网络动力学模型的附加线性层，并引入L2范数有界偏置项以处理高阶余量。基于不同神经动力学模型和安全约束的综合实验表明：在保证安全性的前提下，采用可靠近似的神经网络动力学模型比基于混合整数规划的安全控制基线快10-100倍，验证了最坏情况安全指标的有效性及所提BOND方法在大规模实时场景中的可扩展性。代码开源发布于https://github.com/intelligent-control-lab/BOND。