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arXiv · 2604.08521

Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality

Robert H. Moldenhauer·Karl Worthmann·Romain Postoyan·Dragan Nešić·Mathieu Granzotto
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Abstract

We study closed-loop stability and suboptimality for MPC and infinite-horizon optimal control solved using a surrogate model that differs from the real plant. We employ a unified framework based on quadratic costs to analyze both finite- and infinite-horizon problems, encompassing discounted and undiscounted scenarios alike. Plant-model mismatch bounds proportional to states and controls are assumed, under which the origin remains an equilibrium. Under continuity of the model and cost-controllability, exponential stability of the closed loop can be guaranteed. Furthermore, we give a suboptimality bound for the closed-loop cost recovering the optimal cost of the surrogate. The results reveal a tradeoff between horizon length, discounting and plant-model mismatch. The robustness guarantees are uniform over the horizon length, meaning that larger horizons do not require successively smaller plant-model mismatch.

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Robert H. Moldenhauer, Karl Worthmann, Romain Postoyan, Dragan Nešić, Mathieu Granzotto. 2026-04-09. Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality. https://arxiv.org/abs/2604.08521

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