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

Author(s):

R. Gondhalekar, C.N. Jones
Conference/Journal:

Automatica, vol. 47, pp. 326-333
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.

Year:

2010
Type of Publication:

(01)Article
Supervisor:

M. Morari

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% Autogenerated BibTeX entry
@Article { GonJon:2010:IFA_3721,
    author={R. Gondhalekar and C.N. Jones},
    title={{MPC of constrained discrete-time linear periodic systems 
	  A framework for asynchronous control: Strong feasibility,
	  stability and optimality via periodic invariance}},
    journal={Automatica},
    year={2010},
    volume={47},
    number={},
    pages={326--333},
    month=dec,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=3721}
}
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