Residual Learning-Based Control of Vehicle Platoons with ${\mathrm{\ell }}_2$ Stability Guarantees via Recurrent Equilibrium Networks

This paper proposes a residual learning-based control framework for heterogeneous vehicle platoons subject to parametric uncertainty and external disturbances. A nominal controller designed via Linear Matrix Inequalities (LMIs), along with disturbance-observer compensation, is enhanced by a Recurrent Equilibrium Network (REN) trained offline using stored trajectories and nominal-model prediction errors. The REN is constrained to satisfy a prescribed ${\mathrm{\ell }}_2$-gain bound, enabling sufficient small-gain conditions for local closed-loop stability and disturbance string stability. Experiments demonstrate reduced spacing and velocity errors relative to the nominal controller.