Stability Analysis of Complementarity Systems with Neural Network Controllers
This addresses stability verification for robotics tasks like locomotion and manipulation, providing a method for systems with non-smooth dynamics, but it is incremental as it builds on existing complementarity and LMI techniques.
The paper tackles the problem of verifying stability in complementarity systems with neural network controllers by representing ReLU networks as linear complementarity problems, enabling stability analysis via linear matrix inequalities, and demonstrates it on multi-contact and friction models.
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.