Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming
Abstract
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these systems is challenging due to the nonlinear and compositional structure of neural networks. In this paper, we propose a novel forward reachability analysis method for the safety verification of linear time-varying systems with neural networks in feedback interconnection. Our technical approach relies on abstracting the nonlinear activation functions by quadratic constraints, which leads to an outer-approximation of forward reachable sets of the closed-loop system. We show that we can compute these approximate reachable sets using semidefinite programming. We illustrate our method in a quadrotor example, in which we first approximate a nonlinear model predictive controller via a deep neural network and then apply our analysis tool to certify finite-time reachability and constraint satisfaction of the closed-loop system.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.07876
- arXiv:
- arXiv:2004.07876
- Bibcode:
- 2020arXiv200407876H
- Keywords:
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- Electrical Engineering and Systems Science - Systems and Control;
- Computer Science - Machine Learning;
- Mathematics - Optimization and Control