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Real-time proximal gradient method for linear MPC*

This paper presents a real-time implementation of the proximal gradient method (PGM) in a model predictive control (MPC) setting. In each control update only one iteration of the PGM is performed, while a next update is warm-started using the solution of the previous one. When applied to linear time-invariant (LTI) systems with simple input constraints, the resulting control law becomes extremely simple and offers possibilities to obtain fast control rates even on resource-constrained hardware. The paper provides a proof of closed-loop stability of the real-time PGM applied to LTI systems. A numerical simulation example validates the resulting closed-loop performance.