Efficient Configuration-Constrained Tube MPC via Variables Restriction and Template Selection

TL;DR

This paper introduces a structured framework and a template refinement algorithm for configuration-constrained tube MPC, significantly reducing computation while maintaining stability, demonstrated through simulations on benchmark and high-dimensional systems.

Contribution

It proposes a novel structured framework and an iterative template refinement algorithm to balance complexity and conservatism in CCTMPC, enhancing real-time applicability.

Findings

Reduced online computation time while retaining stability guarantees

Achieved robust performance with minimal computational overhead

Validated approach on benchmark and high-dimensional systems

Abstract

Configuration-Constrained Tube Model Predictive Control (CCTMPC) offers flexibility by using a polytopic parameterization of invariant sets and the optimization of an associated vertex control law. This flexibility, however, often demands computational trade-offs between set parameterization accuracy and optimization complexity. This paper proposes two innovations that help the user tackle this trade-off. First, a structured framework is proposed, which strategically limits optimization degrees of freedom, significantly reducing online computation time while retaining stability guarantees. This framework aligns with Homothetic Tube MPC (HTMPC) under maximal constraints. Second, a template refinement algorithm that iteratively solves quadratic programs is introduced to balance polytope complexity and conservatism. Simulation studies on an illustrative benchmark problem as well as a high-dimensional ten-state system demonstrate the approach's efficiency, achieving robust performance with minimal computational overhead. The results validate a practical pathway to leveraging CCTMPC's adaptability without sacrificing real-time viability.