Neural Lyapunov Model Predictive Control

This paper presentsNeural Lyapunov MPC, analgorithm to alternately train a Lyapunov neuralnetwork and a stabilising constrained Model Pre-dictive Controller (MPC), given a neural networkmodel of the system dynamics. This extends re-cent works on Lyapunov networks to be able totrain solely from expert demonstrations of one-step transitions. The learned Lyapunov networkis used as the value function for the MPC in orderto guarantee stability and extend the stable region.Formal results are presented on the existence of aset of MPC parameters, such as discount factors,that guarantees stability with a horizon as short asone. Robustness margins are also discussed andexisting performance bounds on value functionMPC are extended to the case of imperfect mod-els. The approach is tested on unstable non-linearcontinuous control tasks with hard constraints.Results demonstrate that, when a neural networktrained on short sequences is used for predictions,a one-step horizon Neural Lyapunov MPC cansuccessfully reproduce the expert behaviour andsignificantly outperform longer horizon MPCs.