Stability proof for nonlinear MPC design using monotonically increasing weighting profiles without terminal constraints
In this note, a new formulation of Model Predictive Control (MPC) framework with no stability-related terminal constraint is proposed and its stability is proved under mild standard assumptions. The novelty in the formulation lies in the use of time-varying monotonically increasing stage cost penalt...
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| Published in | Automatica (Oxford) Vol. 87; pp. 455 - 459 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.01.2018
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0005-1098 1873-2836 |
| DOI | 10.1016/j.automatica.2017.10.002 |
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| Abstract | In this note, a new formulation of Model Predictive Control (MPC) framework with no stability-related terminal constraint is proposed and its stability is proved under mild standard assumptions. The novelty in the formulation lies in the use of time-varying monotonically increasing stage cost penalty. The main result is that the0-reachability prediction horizon can always be made stabilizing without any terminal constraints provided that the increasing rate of the penalty is made sufficiently high. Moreover, it is shown through an illustrative example that the time varying penalty may improve the resulting closed-loop performance computed with the original stage-cost when compared to the traditional MPC formulation with final constraint on the state. |
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| AbstractList | In this note, a new formulation of Model Predictive Control (MPC) framework with no stability-related terminal constraint is proposed and its stability is proved under mild standard assumptions. The novelty in the formulation lies in the use of time-varying monotonically increasing stage cost penalty. The main result is that the0-reachability prediction horizon can always be made stabilizing without any terminal constraints provided that the increasing rate of the penalty is made sufficiently high. Moreover, it is shown through an illustrative example that the time varying penalty may improve the resulting closed-loop performance computed with the original stage-cost when compared to the traditional MPC formulation with final constraint on the state. In this note, a new formulation of Model Predictive Control (MPC) framework with no stability-related terminal constraint is proposed and its stability is proved under mild standard assumptions. The novelty in the formulation lies in the use of time-varying monotonically increasing stage cost penalty. The main result is that the 0-reachability prediction horizon can always be made stabilizing without any terminal constraints provided that the increasing rate of the penalty is made sufficiently high. Moreover, it is shown through an illustrative example that the time varying penalty may improve the resulting closed-loop performance computed with the original stage-cost when compared to the traditional MPC formulation with final constraint on the state. |
| Author | Alamir, Mazen |
| Author_xml | – sequence: 1 givenname: Mazen surname: Alamir fullname: Alamir, Mazen email: mazen.alamir@grenoble-inp.fr organization: CNRS, Univ. Grenoble Alpes, Gipsa-lab, F-3800, Grenoble, France |
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| Cites_doi | 10.1007/BF00938540 10.1016/j.automatica.2016.09.045 10.1109/TAC.2005.847055 10.1016/S0005-1098(99)00214-9 10.1137/090758696 10.1016/0167-6911(94)90051-5 10.1016/j.jprocont.2017.09.006 10.1109/TAC.2005.846597 10.1016/j.sysconle.2014.08.002 10.1109/9.57020 10.1016/0005-1098(95)00042-U |
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| Keywords | Nonlinear System Model predicitive control stability |
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| References | Grüne, Pannek, Seehafer, Worthmann (b9) 2010; 48 Alamir, Bornard (b5) 1995; 31 Mayne, Michalska (b13) 1990; 35 Alamir (b1) 2007 Alamir (b2) 2017; 75 Alamir, Bonnay, Bonne, Trinh (b3) 2017 Boccia, Grüne, Worthmann (b6) 2014; 72 Mayne, Rawlings, Rao, Scokaert (b14) 2000; 36 Alamir, Bornard (b4) 1994; 23 Kothare, de Oliveira, Morari (b12) 2000; 45 Grimm, Messina, Tuna, Teel (b7) 2005; 50 Grüne, Pannek (b8) 2011 Keerthi, Gilbert (b11) 1988; 57 Jadbabaie, Hauser (b10) 2005; 50 Keerthi (10.1016/j.automatica.2017.10.002_b11) 1988; 57 Alamir (10.1016/j.automatica.2017.10.002_b5) 1995; 31 Grüne (10.1016/j.automatica.2017.10.002_b8) 2011 Mayne (10.1016/j.automatica.2017.10.002_b14) 2000; 36 Boccia (10.1016/j.automatica.2017.10.002_b6) 2014; 72 Jadbabaie (10.1016/j.automatica.2017.10.002_b10) 2005; 50 Alamir (10.1016/j.automatica.2017.10.002_b3) 2017 Grüne (10.1016/j.automatica.2017.10.002_b9) 2010; 48 Grimm (10.1016/j.automatica.2017.10.002_b7) 2005; 50 Kothare (10.1016/j.automatica.2017.10.002_b12) 2000; 45 Mayne (10.1016/j.automatica.2017.10.002_b13) 1990; 35 Alamir (10.1016/j.automatica.2017.10.002_b1) 2007 Alamir (10.1016/j.automatica.2017.10.002_b2) 2017; 75 Alamir (10.1016/j.automatica.2017.10.002_b4) 1994; 23 |
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| Snippet | In this note, a new formulation of Model Predictive Control (MPC) framework with no stability-related terminal constraint is proposed and its stability is... |
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| Title | Stability proof for nonlinear MPC design using monotonically increasing weighting profiles without terminal constraints |
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