RNN Controller for Lane-Keeping Systems with Robustness and Safety Verification

TL;DR

This paper develops a robust RNN-based lane-keeping controller that guarantees stability and safety despite uncertainties and disturbances, validated through semidefinite programming and numerical experiments.

Contribution

It introduces a novel framework combining quadratic constraints and linear fractional transformations to analyze and verify RNN controllers for vehicle lane-keeping systems.

Findings

Proves robust stability of the RNN controller under uncertain vehicle speeds.

Defines a reachable set and verifies safety via semidefinite programming.

Demonstrates effectiveness on untrained datasets with varying road conditions.

Abstract

This paper proposes a Recurrent Neural Network (RNN) controller for lane-keeping systems, effectively handling model uncertainties and disturbances. First, quadratic constraints cover the nonlinearities brought by the RNN controller, and the linear fractional transformation method models the dynamics of system uncertainties. Second, we prove the robust stability of the lane-keeping system in the presence of uncertain vehicle speed using a linear matrix inequality. Then, we define a reachable set for the lane-keeping system. Finally, to confirm the safety of the lane-keeping system with tracking error bound, we formulate semidefinite programming to approximate the outer set of the reachable set. Numerical experiments demonstrate that this approach confirms the stabilizing RNN controller and validates the safety with an untrained dataset with untrained varying road curvatures.