Accelerating soft-constrained MPC for linear systems through online constraint removal

TL;DR

This paper introduces an online constraint removal method for soft-constrained MPC in linear systems, significantly reducing computational time while maintaining control performance, demonstrated on a thermal model.

Contribution

It extends constraint-adaptive MPC to soft constraints by using predicted input sequences for constraint removal, enabling faster optimization.

Findings

Achieved three orders of magnitude reduction in computational time.

Maintained control accuracy with constraint removal.

Validated on a thermal transport model.

Abstract

Optimization-based controllers, such as Model Predictive Control (MPC), have attracted significant research interest due to their intuitive concept, constraint handling capabilities, and natural application to multi-input multi-output systems. However, the computational complexity of solving a receding horizon problem at each time step remains a challenge for the deployment of MPC. This is particularly the case for systems constrained by many inequalities. Recently, we introduced the concept of constraint-adaptive MPC (ca-MPC) to address this challenge for linear systems with hard constraints. In ca-MPC, at each time step, a subset of the constraints is removed from the optimization problem, thereby accelerating the optimization procedure, while resulting in identical closed-loop behavior. The present paper extends this framework to soft-constrained MPC by detecting and removing constraints based on sub-optimal predicted input sequences, which is rather easy for soft-constrained MPC due to the receding horizon principle and the inclusion of slack variables. We will translate these new ideas explicitly to an offset-free output tracking problem. The effectiveness of these ideas is demonstrated on a two-dimensional thermal transport model, showing a three order of magnitude improvement in online computational time of the MPC scheme.