Efficient configuration-constrained tube MPC via variables restriction and template selection

Configuration-Constrained Tube Model Predictive Control (CCTMPC) offers flexibility through polytopic parameterization of invariant sets and optimization of an associated vertex control law. However, this flexibility introduces a tradeoff between set accuracy and computational complexity. This paper addresses it with two contributions. First, a structured framework is proposed that restricts optimization degrees of freedom in a systematic way, significantly reducing online computation while retaining stability guarantees. This framework aligns with Homothetic Tube MPC (HTMPC) under maximal constraints. Second, a template refinement algorithm is introduced, which iteratively solves quadratic programs to balance polytope complexity and conservatism. Simulations on an illustrative benchmark and a high-dimensional tenstate system demonstrate the contributions' efficiency, achieving robust performance with minimal computational overhead. The results validate a practical pathway to exploit CCTMPC's adaptability without compromising real-time viability.