Brief paper: MPC of constrained discrete-time linear periodic systems - A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

  • Authors:

  • Ravi Gondhalekar;Colin N. Jones

  • Affiliations:

  • Department of Mechanical Engineering and Frontier Research Base for Global Young Researchers, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita-shi, Osaka, 565-0871, Japan;Automatic Control Laboratory, Department of Electrical Engineering, Swiss Federal Institute of Technology in Zurich (ETHZ), ETL I 28, Physikstrasse 3, 8092 Zurich, Switzerland

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2011

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Abstract

State-feedback model predictive control (MPC) of discrete-time linear periodic systems with time-dependent state and input dimensions is considered. The states and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. First, periodic controlled and positively invariant sets are characterized, and a method to determine the maximum periodic controlled and positively invariant sets is derived. The proposed periodic controlled invariant sets are then employed in the design of least-restrictive strongly feasible reference-tracking MPC problems. The proposed periodic positively invariant sets are employed in combination with well-known results on optimal unconstrained periodic linear-quadratic regulation (LQR) to yield constrained periodic LQR control laws that are stabilizing and optimal. One motivation for systems with time-dependent dimensions is efficient control law synthesis for discrete-time systems with asynchronous inputs, for which a novel modeling framework resulting in low dimensional models is proposed. The presented methods are applied to a multirate nano-positioning system.