Learning Neural Network Safe Tracking Controllers from Backward Reachable Sets

TL;DR

This paper introduces a neural network-based safe tracking control method for nonlinear discrete-time systems, utilizing backward reachable sets and formal verification to ensure safety and robustness in the presence of disturbances.

Contribution

It presents a novel framework combining backward reachable sets with neural network training for safe tracking control of nonlinear systems.

Findings

Successfully guarantees safety using backward reachable sets.

Achieves formal safety verification with conformal prediction.

Demonstrates effectiveness on a discrete-time Dubin's car model.

Abstract

The design of tracking controllers that closely follow a reference trajectory while ensuring safety and robustness against disturbances is a challenging problem in the control of autonomous systems. In this work, we propose a neural network-based safe tracking control framework for nonlinear discrete-time systems with reach-avoid specifications in the presence of disturbances. Our approach begins with generation of a nominal trajectory using standard trajectory synthesis approaches, followed by construction of safe zonotopic backward reachable sets along the nominal trajectory. The states lying within the backward reachable sets are guaranteed to satisfy safe reachability specifications. Then, our key insight is to leverage the computed backward reachable sets to inform the architecture and training of a neural network-based tracking controller such that the neural network drives the system's states through these backward reachable sets, thereby improving the likelihood of safe reachability. We perform formal verification with conformal prediction to achieve statistical safety guarantees on the performance of the learned neural controller. The performance of our approach is illustrated through a numerical example on the discrete-time Dubin's car model.