Configuration-Constrained Tube MPC for Periodic Operation

Periodic operation often emerges as the economically optimal mode in industrial processes, particularly under varying economic or environmental conditions. This paper proposes a robust model predictive control (MPC) framework for uncertain systems modeled as polytopic linear differential inclusions (LDIs), where the dynamics evolve as convex combinations of finitely many affine control systems with additive disturbances. The robust control problem is reformulated as a convex optimization program by optimizing over configuration-constrained polytopic tubes and tracks a periodic trajectory that is optimal for a given economic criterion. Artificial variables embedded in the formulation ensure recursive feasibility and robust constraint satisfaction when the economic criterion is updated online, while guaranteeing convergence to the corresponding optimal periodic tube when the criterion remains constant. To improve computational efficiency, we introduce a quadratic over-approximation of the periodic cost under a Lipschitz continuity assumption, yielding a Quadratic Program (QP) formulation that preserves the above theoretical guarantees. The effectiveness and scalability of the approach are demonstrated on a benchmark example and a ball-plate system with eight states.