Brief paper: Controlled invariant feasibility - A general approach to enforcing strong feasibility in MPC applied to move-blocking

  • Authors:

  • Ravi Gondhalekar;Jun-ichi Imura;Kenji Kashima

  • Affiliations:

  • Department of Mechanical Engineering and Frontier Research Base for Global Young Researchers, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita-shi 565-0871, Osaka, Japan;Department of Mechanical and Environmental Informatics, Graduate School of Information Science and Engineering, Tokyo Institute of Technology, 2-12-1-W8 Oo-Okayama, Meguro-ku 152-8552, Tokyo, Japa ...;Department of Mechanical and Environmental Informatics, Graduate School of Information Science and Engineering, Tokyo Institute of Technology, 2-12-1-W8 Oo-Okayama, Meguro-ku 152-8552, Tokyo, Japa ...

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

Strong feasibility of MPC problems is usually enforced by constraining the state at the final prediction step to a controlled invariant set. However, such terminal constraints fail to enforce strong feasibility in a rich class of MPC problems, for example when employing move-blocking. In this paper a generalized, least restrictive approach for enforcing strong feasibility of MPC problems is proposed and applied to move-blocking MPC. The approach hinges on the novel concept of controlled invariant feasibility. Instead of a terminal constraint, the state of an earlier prediction step is constrained to a controlled invariant feasible set. Controlled invariant feasibility is a generalization of controlled invariance. The convergence of well-known approaches for determining maximum controlled invariant sets, and j-step admissible sets, is formally proved. Thus an algorithm for rigorously approximating maximum controlled invariant feasible sets is developed for situations where the exact maximum cannot be determined.