Safe Control with Neural Network Dynamic Models

• URL: http://arxiv.org/abs/2110.01110v1
• Date: Sun, 3 Oct 2021 22:13:49 GMT
• Title: Safe Control with Neural Network Dynamic Models
• Authors: Tianhao Wei and Changliu Liu
• Abstract summary: We propose MIND-SIS, the first method to derive safe control laws for Neural Network Dynamic Models (NNDM) MIND-SIS guarantees forward invariance and finite convergence. It has been numerically validated that MIND-SIS achieves safe and optimal control of NNDM.
• Score: 2.512827436728378
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Safety is critical in autonomous robotic systems. A safe control law ensures forward invariance of a safe set (a subset in the state space). It has been extensively studied regarding how to derive a safe control law with a control-affine analytical dynamic model. However, in complex environments and tasks, it is challenging and time-consuming to obtain a principled analytical model of the system. In these situations, data-driven learning is extensively used and the learned models are encoded in neural networks. How to formally derive a safe control law with Neural Network Dynamic Models (NNDM) remains unclear due to the lack of computationally tractable methods to deal with these black-box functions. In fact, even finding the control that minimizes an objective for NNDM without any safety constraint is still challenging. In this work, we propose MIND-SIS (Mixed Integer for Neural network Dynamic model with Safety Index Synthesis), the first method to derive safe control laws for NNDM. The method includes two parts: 1) SIS: an algorithm for the offline synthesis of the safety index (also called as barrier function), which uses evolutionary methods and 2) MIND: an algorithm for online computation of the optimal and safe control signal, which solves a constrained optimization using a computationally efficient encoding of neural networks. It has been theoretically proved that MIND-SIS guarantees forward invariance and finite convergence. And it has been numerically validated that MIND-SIS achieves safe and optimal control of NNDM. From our experiments, the optimality gap is less than $10^{-8}$, and the safety constraint violation is $0$.

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