記号的微分界伝播によるニューラル制御バリア関数の検証
Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation
ReLUベースのニューラル制御バリア関数を、活性化関数の微分をヘヴィサイド関数として扱い、ヤコビアンと非線形システム動力学の内積を通じて記号的に界を伝播させる効率的な検証フレームワークを提案した。
著者: Hanjiang Hu, Yujie Yang, Tianhao Wei, Changliu Liu
分類: cs.RO, cs.LG, cs.SY, eess.SY, math.OC
原文アブストラクト
Control barrier functions (CBFs) are important in safety-critical systems and robot control applications. Neural networks have been used to parameterize and synthesize CBFs with bounded control input for complex systems. However, it is still challenging to verify pre-trained neural networks CBFs (neural CBFs) in an efficient symbolic manner. To this end, we propose a new efficient verification framework for ReLU-based neural CBFs through symbolic derivative bound propagation by combining the linearly bounded nonlinear dynamic system and the gradient bounds of neural CBFs. Specifically, with Heaviside step function form for derivatives of activation functions, we show that the symbolic bounds can be propagated through the inner product of neural CBF Jacobian and nonlinear system dynamics. Through extensive experiments on different robot dynamics, our results outperform the interval arithmetic based baselines in verified rate and verification time along the CBF boundary, validating the effectiveness and efficiency of the proposed method with different model complexity. The code can be found at https://github.com/intelligent-control-lab/ verify-neural-CBF.
