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Predictive safety filters provide a way of projecting potentially unsafeinputs onto the set of inputs that guarantee recursive state and inputconstraint satisfaction. Unsafe inputs, proposed, e.g. by a human orlearning-based controller, can thereby be filtered by leveraging modelpredictive control techniques. In this paper, we extend this framework suchthat in addition, robust asymptotic stability of the closed-loop system can beguaranteed by enforcing a decrease of an implicit Lyapunov function which isconstructed using a predicted system trajectory. Differently from previousresults, we show robust asymptotic stability on an extended state consisting ofthe system state and a warmstart input sequence and establish robust asymptoticstability for the augmented dynamics with respect to a predefined disturbance.The proposed strategy is applied to an automotive lane keeping example insimulation.

Predictive stability filters for nonlinear dynamical systems affected by disturbances