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.

翻译：神经网络动态模型（NNDMs）的安全控制对机器人技术及众多应用领域至关重要。然而，实时计算NNDM的最优安全控制仍具挑战。为支持实时计算，我们提出在控制综合中使用NNDM的合理近似。具体而言，我们基于伯恩斯坦多项式过近似（BPO）对NNDM中的ReLU激活函数进行逼近，提出了伯恩斯坦过近似神经动力学（BOND）。为减小近似引入的误差并确保安全控制问题的持续可行性，我们利用NNDM的BPO松弛范围内最不安全近似状态，离线综合出最坏情况安全指数。针对在线实时优化，我们将非线性最坏情况安全约束的一阶泰勒近似构建为NNDM的额外线性层，其高阶余项由l2有界偏置项表示。通过在不同神经动力学与安全约束下的综合实验证明：在保证安全性的前提下，采用合理近似的NNDM比基于混合整数规划（MIP）的安全控制基线快10-100倍，验证了最坏情况安全指数的有效性及所提BOND在实时大规模场景中的可扩展性。