Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC
Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Norwegian Society of Automatic Control
2010-04-01
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| Series: | Modeling, Identification and Control |
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| Online Access: | http://www.mic-journal.no/PDF/2010/MIC-2010-2-1.pdf |
| _version_ | 1818807550839095296 |
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| author | Morten Hovd Sorin Olaru |
| author_facet | Morten Hovd Sorin Olaru |
| author_sort | Morten Hovd |
| collection | DOAJ |
| description | Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ) Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC). A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general. |
| first_indexed | 2024-12-18T19:27:27Z |
| format | Article |
| id | doaj.art-e706b9fcffab45b78a8e79c481e5bba9 |
| institution | Directory Open Access Journal |
| issn | 0332-7353 1890-1328 |
| language | English |
| last_indexed | 2024-12-18T19:27:27Z |
| publishDate | 2010-04-01 |
| publisher | Norwegian Society of Automatic Control |
| record_format | Article |
| series | Modeling, Identification and Control |
| spelling | doaj.art-e706b9fcffab45b78a8e79c481e5bba92022-12-21T20:55:49ZengNorwegian Society of Automatic ControlModeling, Identification and Control0332-73531890-13282010-04-01312455310.4173/mic.2010.2.1Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPCMorten HovdSorin OlaruExplicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ) Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC). A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.http://www.mic-journal.no/PDF/2010/MIC-2010-2-1.pdfPiecewise Quadratic Lyapunov functionLinear Matrix InequalitiesModel Predictive Control |
| spellingShingle | Morten Hovd Sorin Olaru Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC Modeling, Identification and Control Piecewise Quadratic Lyapunov function Linear Matrix Inequalities Model Predictive Control |
| title | Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC |
| title_full | Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC |
| title_fullStr | Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC |
| title_full_unstemmed | Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC |
| title_short | Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC |
| title_sort | piecewise quadratic lyapunov functions for stability verification of approximate explicit mpc |
| topic | Piecewise Quadratic Lyapunov function Linear Matrix Inequalities Model Predictive Control |
| url | http://www.mic-journal.no/PDF/2010/MIC-2010-2-1.pdf |
| work_keys_str_mv | AT mortenhovd piecewisequadraticlyapunovfunctionsforstabilityverificationofapproximateexplicitmpc AT sorinolaru piecewisequadraticlyapunovfunctionsforstabilityverificationofapproximateexplicitmpc |