Stochastic MPC with dynamic feedback gain selection and discounted probabilistic constraints
This paper considers linear discrete-time systems with additive disturbances, and designs an MPC law incorporating a dynamic feedback gain to minimise a quadratic cost function subject to a single chance constraint. The feedback gain is selected online and we provide two selection methods based on m...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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IEEE
2021
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| _version_ | 1797108541201317888 |
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| author | Yan, S Goulart, PJ Cannon, M |
| author_facet | Yan, S Goulart, PJ Cannon, M |
| author_sort | Yan, S |
| collection | OXFORD |
| description | This paper considers linear discrete-time systems with additive disturbances, and designs an MPC law incorporating a dynamic feedback gain to minimise a quadratic cost function subject to a single chance constraint. The feedback gain is selected online and we provide two selection methods based on minimising upper bounds on predicted costs. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and assigning violation probabilities in the far future with vanishingly small weights, this form of constraints allows for an MPC law with guarantees of recursive feasibility without a boundedness assumption on the disturbance. A computationally convenient MPC optimisation problem is formulated using Chebyshev's inequality and we introduce an online constraint-tightening technique to ensure recursive feasibility. The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition. With dynamic feedback gain selection, the closed loop cost is reduced and conservativeness of Chebyshev's inequality is mitigated.
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| first_indexed | 2024-03-07T07:30:32Z |
| format | Journal article |
| id | oxford-uuid:8afdd4f3-9aad-4ef1-9769-320c49052403 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:30:32Z |
| publishDate | 2021 |
| publisher | IEEE |
| record_format | dspace |
| spelling | oxford-uuid:8afdd4f3-9aad-4ef1-9769-320c490524032023-01-11T07:44:40ZStochastic MPC with dynamic feedback gain selection and discounted probabilistic constraintsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8afdd4f3-9aad-4ef1-9769-320c49052403EnglishSymplectic ElementsIEEE2021Yan, SGoulart, PJCannon, MThis paper considers linear discrete-time systems with additive disturbances, and designs an MPC law incorporating a dynamic feedback gain to minimise a quadratic cost function subject to a single chance constraint. The feedback gain is selected online and we provide two selection methods based on minimising upper bounds on predicted costs. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and assigning violation probabilities in the far future with vanishingly small weights, this form of constraints allows for an MPC law with guarantees of recursive feasibility without a boundedness assumption on the disturbance. A computationally convenient MPC optimisation problem is formulated using Chebyshev's inequality and we introduce an online constraint-tightening technique to ensure recursive feasibility. The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition. With dynamic feedback gain selection, the closed loop cost is reduced and conservativeness of Chebyshev's inequality is mitigated. |
| spellingShingle | Yan, S Goulart, PJ Cannon, M Stochastic MPC with dynamic feedback gain selection and discounted probabilistic constraints |
| title | Stochastic MPC with dynamic feedback gain selection and discounted probabilistic constraints |
| title_full | Stochastic MPC with dynamic feedback gain selection and discounted probabilistic constraints |
| title_fullStr | Stochastic MPC with dynamic feedback gain selection and discounted probabilistic constraints |
| title_full_unstemmed | Stochastic MPC with dynamic feedback gain selection and discounted probabilistic constraints |
| title_short | Stochastic MPC with dynamic feedback gain selection and discounted probabilistic constraints |
| title_sort | stochastic mpc with dynamic feedback gain selection and discounted probabilistic constraints |
| work_keys_str_mv | AT yans stochasticmpcwithdynamicfeedbackgainselectionanddiscountedprobabilisticconstraints AT goulartpj stochasticmpcwithdynamicfeedbackgainselectionanddiscountedprobabilisticconstraints AT cannonm stochasticmpcwithdynamicfeedbackgainselectionanddiscountedprobabilisticconstraints |