On the convergence of stochastic MPC to terminal modes of operation
The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of the state, but convergence to a terminal control law is typi...
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| Format: | Conference item |
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Institute of Electrical and Electronics Engineers
2019
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| _version_ | 1826269591012114432 |
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| author | Munoz-Carpintero, D Cannon, M |
| author_facet | Munoz-Carpintero, D Cannon, M |
| author_sort | Munoz-Carpintero, D |
| collection | OXFORD |
| description | The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of the state, but convergence to a terminal control law is typically not shown. In this work we use results on general state space Markov chains to find conditions that guarantee convergence of disturbed nonlinear systems to terminal modes of operation, so that they converge in probability to a priori known terminal linear feedback laws and achieve time-average performance equal to that of the terminal control law. We discuss implications for the convergence of control laws in stochastic MPC formulations, in particular we prove convergence for two formulations of stochastic MPC. |
| first_indexed | 2024-03-06T21:27:28Z |
| format | Conference item |
| id | oxford-uuid:43934763-3183-47a9-8d35-0b7aa542a7e3 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:27:28Z |
| publishDate | 2019 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | oxford-uuid:43934763-3183-47a9-8d35-0b7aa542a7e32022-03-26T14:56:19ZOn the convergence of stochastic MPC to terminal modes of operationConference itemhttp://purl.org/coar/resource_type/c_5794uuid:43934763-3183-47a9-8d35-0b7aa542a7e3Symplectic Elements at OxfordInstitute of Electrical and Electronics Engineers2019Munoz-Carpintero, DCannon, MThe stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of the state, but convergence to a terminal control law is typically not shown. In this work we use results on general state space Markov chains to find conditions that guarantee convergence of disturbed nonlinear systems to terminal modes of operation, so that they converge in probability to a priori known terminal linear feedback laws and achieve time-average performance equal to that of the terminal control law. We discuss implications for the convergence of control laws in stochastic MPC formulations, in particular we prove convergence for two formulations of stochastic MPC. |
| spellingShingle | Munoz-Carpintero, D Cannon, M On the convergence of stochastic MPC to terminal modes of operation |
| title | On the convergence of stochastic MPC to terminal modes of operation |
| title_full | On the convergence of stochastic MPC to terminal modes of operation |
| title_fullStr | On the convergence of stochastic MPC to terminal modes of operation |
| title_full_unstemmed | On the convergence of stochastic MPC to terminal modes of operation |
| title_short | On the convergence of stochastic MPC to terminal modes of operation |
| title_sort | on the convergence of stochastic mpc to terminal modes of operation |
| work_keys_str_mv | AT munozcarpinterod ontheconvergenceofstochasticmpctoterminalmodesofoperation AT cannonm ontheconvergenceofstochasticmpctoterminalmodesofoperation |