Offset-free model predictive control: stability under plant-model mismatch
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| Format: | Preprint |
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2024
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| author | Kuntz, Steven J. Rawlings, James B. |
| author_facet | Kuntz, Steven J. Rawlings, James B. |
| contents | We present the first general stability results for nonlinear offset-free model predictive control (MPC). Despite over twenty years of active research, the offset-free MPC literature has not shaken the assumption of closed-loop stability for establishing offset-free performance. In this paper, we present a nonlinear offset-free MPC design that is robustly stable with respect to the tracking errors, and thus achieves offset-free performance, despite plant-model mismatch and persistent disturbances. Key features and assumptions of this design include quadratic costs, differentiability of the plant and model functions, constraint backoffs at steady state, and a robustly stable state and disturbance estimator. We first establish nominal stability and offset-free performance. Then, robustness to state and disturbance estimate errors and setpoint and disturbance changes is demonstrated. Finally, the results are extended to sufficiently small plant-model mismatch. The results are illustrated by numerical examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_08104 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Offset-free model predictive control: stability under plant-model mismatch Kuntz, Steven J. Rawlings, James B. Systems and Control Optimization and Control 93B45, 93D09, 93D30 We present the first general stability results for nonlinear offset-free model predictive control (MPC). Despite over twenty years of active research, the offset-free MPC literature has not shaken the assumption of closed-loop stability for establishing offset-free performance. In this paper, we present a nonlinear offset-free MPC design that is robustly stable with respect to the tracking errors, and thus achieves offset-free performance, despite plant-model mismatch and persistent disturbances. Key features and assumptions of this design include quadratic costs, differentiability of the plant and model functions, constraint backoffs at steady state, and a robustly stable state and disturbance estimator. We first establish nominal stability and offset-free performance. Then, robustness to state and disturbance estimate errors and setpoint and disturbance changes is demonstrated. Finally, the results are extended to sufficiently small plant-model mismatch. The results are illustrated by numerical examples. |
| title | Offset-free model predictive control: stability under plant-model mismatch |
| topic | Systems and Control Optimization and Control 93B45, 93D09, 93D30 |
| url | https://arxiv.org/abs/2412.08104 |