Regret Analysis of Shrinking Horizon Model Predictive Control

This paper analyzes the suboptimal implementation of Shrinking Horizon Model Predictive Control (SHMPC) when a fixed number of solver iterations and a warm-start are utilized at each time step to solve the underlying Optimal Control Problem (OCP). We derive bounds on the loss of performance (regret) and on the difference between suboptimal SHMPC and optimal solutions. This analysis provides insights and practical guidelines for the implementation of SHMPC under computational limitations. A numerical example of axisymmetric spacecraft spin stabilization is reported. The suboptimal implementation of SHMPC is shown to be capable of steering the system from an initial state into a known terminal set while satisfying control constraints.