From Certification of Algorithms To Certified MPC: The Missing Links*

Deriving certification bounds for optimization algorithms is an active research area in the control community. This is mainly impulsed by the use of on-line optimization algorithms in real-time MPC through limited computation power. However, the way such bounds are then used to derive a convergence certification for MPC frameworks is still not suficiently mature. This paper contributes in clarifying what are the unavoidable additional ingredients that need to be combined with any algorithm's certification bound in order to derive a relevant certification result for the MPC-based closed-loop performance. Moreover, the paper gives such a general certification result based on these ingredients for any pair of certified algorithm and provably stable ideal MPC formulation. The proposed framework is then instantiated to the particular case of linear MPC and a simple example is given to illustrate the introduced concepts.