Fast Switching in Mixed-Integer Model Predictive Control
For control engineers using mixed-integer MPC, this provides a theoretical stability guarantee for fast-switching implementations, though the approach is incremental as it extends existing relaxation and rounding techniques.
The paper proves that mixed-integer model predictive control with fast switching can achieve practical asymptotic stability by combining partial outer convexification, binary relaxation, and sum-up rounding on an oversampling grid, enabling efficient integer feasibility while approximating relaxed system behavior arbitrarily closely.
We deduce stability results for finite control set and mixed-integer model predictive control with a downstream oversampling phase. The presentation rests upon the inherent robustness of model predictive control with stabilizing terminal conditions and techniques for solving mixed-integer optimal control problems by continuous optimization. Partial outer convexification and binary relaxation transform mixed-integer problems into common optimal control problems. We deduce nominal asymptotic stability for the resulting relaxed system formulation and implement sum-up rounding to restore efficiently integer feasibility on an oversampling time grid. If fast control switching is technically possible and inexpensive, we can approximate the relaxed system behavior in the state space arbitrarily close. We integrate input perturbed model predictive control with practical asymptotic stability. Numerical experiments illustrate practical relevance of fast control switching.