Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917396351025152 |
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| author | Moldenhauer, Robert H. Worthmann, Karl Postoyan, Romain Nešić, Dragan Granzotto, Mathieu |
| author_facet | Moldenhauer, Robert H. Worthmann, Karl Postoyan, Romain Nešić, Dragan Granzotto, Mathieu |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_08521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality Moldenhauer, Robert H. Worthmann, Karl Postoyan, Romain Nešić, Dragan Granzotto, Mathieu Optimization and Control Systems and Control 93B45 (Primary) 49L20, 93D30 (Secondary) 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. |
| title | Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality |
| topic | Optimization and Control Systems and Control 93B45 (Primary) 49L20, 93D30 (Secondary) |
| url | https://arxiv.org/abs/2604.08521 |