MPC without Terminal Ingredients Tailored to the SEIR Compartmental Epidemic Model
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917689072549888 |
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| author | Esterhuizen, Willem Sauerteig, Philipp Streif, Stefan Worthmann, Karl |
| author_facet | Esterhuizen, Willem Sauerteig, Philipp Streif, Stefan Worthmann, Karl |
| contents | We consider the SEIR compartmental epidemic model subject to state and input constraints (a cap on the proportion of infectious individuals and limits on the allowed social distancing and quarantining measures, respectively). We present a tailored model predictive control (MPC) scheme without terminal conditions. We rigorously show recursive feasibility and asymptotic convergence of the MPC closed loop to the continuum of disease-free equilibrium points for suitably designed quadratic running cost and a sufficiently long prediction horizon (forecast window). Moreover, we establish the viability kernel (a.k.a. the admissible set) as a domain of attraction of the continuum of equilibria. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_09151 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | MPC without Terminal Ingredients Tailored to the SEIR Compartmental Epidemic Model Esterhuizen, Willem Sauerteig, Philipp Streif, Stefan Worthmann, Karl Optimization and Control Systems and Control 93B45 (primary), 34H05, 49N90, 93C10 We consider the SEIR compartmental epidemic model subject to state and input constraints (a cap on the proportion of infectious individuals and limits on the allowed social distancing and quarantining measures, respectively). We present a tailored model predictive control (MPC) scheme without terminal conditions. We rigorously show recursive feasibility and asymptotic convergence of the MPC closed loop to the continuum of disease-free equilibrium points for suitably designed quadratic running cost and a sufficiently long prediction horizon (forecast window). Moreover, we establish the viability kernel (a.k.a. the admissible set) as a domain of attraction of the continuum of equilibria. |
| title | MPC without Terminal Ingredients Tailored to the SEIR Compartmental Epidemic Model |
| topic | Optimization and Control Systems and Control 93B45 (primary), 34H05, 49N90, 93C10 |
| url | https://arxiv.org/abs/2403.09151 |