Implementation of soft-constrained MPC for Tracking using its semi-banded problem structure
Victor Gracia, Pablo Krupa, Daniel Limon, Teodoro Alamo
TL;DR
The paper addresses feasibility issues in MPC, focusing on MPCT and proposing a soft-constraint encoding that preserves the semi-banded problem structure. An ADMM-based solver exploits this structure, using a Woodbury-based decomposition to keep online complexity linear in horizon length. Numerical results on a mass-spring system show the approach outperforms generic QP solvers and slack-variable MPCT, while maintaining feasibility even when hard MPCT becomes infeasible. The work offers a practical, fast-solver framework for soft-constrained MPCT with potential impact on fast, constrained tracking applications.
Abstract
Model Predictive Control (MPC) is a popular control approach due to its ability to consider constraints, including input and state restrictions, while minimizing a cost function. However, in practice, these constraints can result in feasibility issues, either because the system model is not accurate or due to the existence of external disturbances. To mitigate this problem, a solution adopted by the MPC community is the use of soft constraints. In this article, we consider a not-so-typical methodology to encode soft constraints in a particular MPC formulation known as MPC for Tracking (MPCT), which has several advantages when compared to standard MPC formulations. The motivation behind the proposed encoding is to maintain the semi-banded structure of the ingredients of a recently proposed solver for the considered MPCT formulation, thus providing an efficient and fast solver when compared to alternative approaches from the literature. We show numerical results highlighting the benefits of the formulation and the computational efficiency of the solver.