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

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