Stabilizing tube-based model predictive control: terminal set and cost construction for LPV systems

J. Hanema, M. Lazar, R. Toth

Research output: Contribution to journalArticleAcademicpeer-review

35 Citations (Scopus)
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This paper presents a stabilizing tube-based MPC synthesis for LPV systems. We employ terminal constraint sets which are required to be controlled periodically contractive. Periodically (or finite-step) contractive sets are easier to compute and can be of lower complexity than “true” contractive ones, lowering the required computational effort both off-line and on-line. Under certain assumptions on the tube parameterization, recursive feasibility of the scheme is proven. Subsequently, asymptotic stability of the origin is guaranteed through the construction of a suitable terminal cost based on a novel Lyapunov-like metric for compact convex sets containing the origin. A periodic variant on the well-known homothetic tube parameterization that satisfies the necessary assumptions and yields a tractable LPV MPC algorithm is derived. The resulting MPC algorithm requires the on-line solution of a single linear program with linear complexity in the prediction horizon. The properties of the approach are demonstrated by a numerical example.
Original languageEnglish
Pages (from-to)137-144
Number of pages8
Publication statusPublished - Nov 2017


  • Linear parameter-varying systems
  • Periodic invariance
  • Tube model predictive control


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