Configuration-Constrained Tube MPC for Periodic Operation

TL;DR

This paper introduces a robust, configuration-constrained tube MPC framework for periodic operation in uncertain systems, optimizing economic criteria with guarantees of feasibility and convergence, and demonstrating effectiveness on benchmark and physical systems.

Contribution

It develops a novel convex optimization-based tube MPC method that handles uncertainties, enforces periodicity, and improves computational efficiency via a quadratic cost approximation.

Findings

Successfully applied to a benchmark example.

Demonstrated on a ball-plate system with eight states.

Ensures recursive feasibility and convergence to optimal periodic trajectories.

Abstract

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.