Adaptive Relaxation based Non-Conservative Chance Constrained Stochastic MPC
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915202374565888 |
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| author | Ghosh, Avik Cortes-Aguirre, Cristian Chen, Yi-An Khurram, Adil Kleissl, Jan |
| author_facet | Ghosh, Avik Cortes-Aguirre, Cristian Chen, Yi-An Khurram, Adil Kleissl, Jan |
| contents | Chance constrained stochastic model predictive controllers (CC-SMPC) trade off full constraint satisfaction for economical plant performance under uncertainty. Previous CC-SMPC works are over-conservative in constraint violations leading to worse economic performance. Other past works require a-priori information about the uncertainty set, limiting their application. This paper considers a discrete LTI system with hard constraints on inputs and chance constraints on states, with unknown uncertainty distribution, statistics, or samples. This work proposes a novel adaptive online update rule to relax the state constraints based on the time-average of past constraint violations, to achieve reduced conservativeness in closed-loop. Under an ideal control policy assumption, it is proven that the time-average of constraint violations asymptotically converges to the maximum allowed violation probability. The method is applied for optimal battery energy storage system (BESS) dispatch in a grid connected microgrid with PV generation and load demand, with chance constraints on BESS state-of-charge (SOC). Realistic simulations show the superior electricity cost saving potential of the proposed method as compared to the traditional economic MPC without chance constraints, and a state-of-the-art approach with chance constraints. We satisfy the chance constraints non-conservatively in closed-loop, effectively trading off increased cost savings with minimal adverse effects on BESS lifetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01973 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive Relaxation based Non-Conservative Chance Constrained Stochastic MPC Ghosh, Avik Cortes-Aguirre, Cristian Chen, Yi-An Khurram, Adil Kleissl, Jan Systems and Control Chance constrained stochastic model predictive controllers (CC-SMPC) trade off full constraint satisfaction for economical plant performance under uncertainty. Previous CC-SMPC works are over-conservative in constraint violations leading to worse economic performance. Other past works require a-priori information about the uncertainty set, limiting their application. This paper considers a discrete LTI system with hard constraints on inputs and chance constraints on states, with unknown uncertainty distribution, statistics, or samples. This work proposes a novel adaptive online update rule to relax the state constraints based on the time-average of past constraint violations, to achieve reduced conservativeness in closed-loop. Under an ideal control policy assumption, it is proven that the time-average of constraint violations asymptotically converges to the maximum allowed violation probability. The method is applied for optimal battery energy storage system (BESS) dispatch in a grid connected microgrid with PV generation and load demand, with chance constraints on BESS state-of-charge (SOC). Realistic simulations show the superior electricity cost saving potential of the proposed method as compared to the traditional economic MPC without chance constraints, and a state-of-the-art approach with chance constraints. We satisfy the chance constraints non-conservatively in closed-loop, effectively trading off increased cost savings with minimal adverse effects on BESS lifetime. |
| title | Adaptive Relaxation based Non-Conservative Chance Constrained Stochastic MPC |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2406.01973 |