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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Bibliographic Details
Published inAutomatica (Oxford) Vol. 87; pp. 455 - 459
Main Author Alamir, Mazen
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.01.2018
Elsevier
Subjects
Automatic
Engineering Sciences
Nonlinear System
Model predicitive control
stability
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ISSN0005-1098
1873-2836
DOI10.1016/j.automatica.2017.10.002

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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2017.10.002