Stability Analysis of Complementarity Systems with Neural Network\n Controllers

2020/11/15 by Alp Aydinoglu, Mahyar Fazlyab, Aydinoglu, Alp +5
Engineering · #Robot Manipulation and Learning #Robotic Mechanisms and Dynamics #Muscle activation and electromyography studies

paper · pdf · doi:10.48550/arxiv.2011.07626

Abstract

Complementarity problems, a class of mathematical optimization problems with\northogonality constraints, are widely used in many robotics tasks, such as\nlocomotion and manipulation, due to their ability to model non-smooth phenomena\n(e.g., contact dynamics). In this paper, we propose a method to analyze the\nstability of complementarity systems with neural network controllers. First, we\nintroduce a method to represent neural networks with rectified linear unit\n(ReLU) activations as the solution to a linear complementarity problem. Then,\nwe show that systems with ReLU network controllers have an equivalent linear\ncomplementarity system (LCS) description. Using the LCS representation, we turn\nthe stability verification problem into a linear matrix inequality (LMI)\nfeasibility problem. We demonstrate the approach on several examples, including\nmulti-contact problems and friction models with non-unique solutions.\n

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