Suboptimal Shrinking Horizon MPC with a Lower Hessian Condition Number from Adjustable Terminal Cost

TL;DR

This paper proposes a dynamic adjustment strategy for shrinking horizon MPC that reduces computational effort by lowering the Hessian condition number, ensuring efficient convergence to a terminal set despite disturbances.

Contribution

It introduces a novel method for adjusting terminal cost and horizon length in SH-MPC to improve computational efficiency and robustness against disturbances.

Findings

Lower Hessian condition number achieved

Reduced number of iterations in MPC

Successful spacecraft nutation damping example

Abstract

A strategy for reducing the number of iterations and computational burden in shrinking horizon Model Predictive Control (SH-MPC) when steering into a prescribed terminal set despite unmeasured disturbances is proposed. This strategy exploits dynamic adjustment of the terminal cost weight and horizon length while ensuring that the terminal set is reached within a desired number of steps. A lower Hessian condition number which facilitates the computational reduction is proved under assumptions, and an example of spacecraft nutation damping using the proposed approach is reported.