论文标题
与神经网络控制器的互补系统的稳定性分析
Stability Analysis of Complementarity Systems with Neural Network Controllers
论文作者
论文摘要
互补性问题是正交性约束的一类数学优化问题，由于它们能够建模非平滑现象（例如接触动力学），因此广泛用于许多机器人技术任务（例如运动和操纵）。在本文中，我们提出了一种分析与神经网络控制器互补系统稳定性的方法。首先，我们介绍了一种表示具有整流线性单元（relu）激活的神经网络的方法，作为解决线性互补问题的解决方案。然后，我们表明具有Relu网络控制器的系统具有等效的线性互补系统（LCS）描述。使用LCS表示，我们将稳定性验证问题变成线性矩阵不等式（LMI）可行性问题。我们在几个示例中演示了这种方法，包括具有非唯一解决方案的多接触问题和摩擦模型。
Complementarity problems, a class of mathematical optimization problems with orthogonality constraints, are widely used in many robotics tasks, such as locomotion and manipulation, due to their ability to model non-smooth phenomena (e.g., contact dynamics). In this paper, we propose a method to analyze the stability of complementarity systems with neural network controllers. First, we introduce a method to represent neural networks with rectified linear unit (ReLU) activations as the solution to a linear complementarity problem. Then, we show that systems with ReLU network controllers have an equivalent linear complementarity system (LCS) description. Using the LCS representation, we turn the stability verification problem into a linear matrix inequality (LMI) feasibility problem. We demonstrate the approach on several examples, including multi-contact problems and friction models with non-unique solutions.
