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The Explicit Linear Quadratic Regulator for Constrained Systems

Author(s):

A. Bemporad, M. Morari, V. Dua, E.N. Pistikopoulos
Conference/Journal:

Automatica, vol. 38, no. 1, pp. 3-20
Abstract:

For discrete time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piecewise linear and continuous for both the finite horizon problem (model predictive control) and the usual infinite time measure (constrained linear quadratic regulation). Thus, the on-line control computation reduces to the simple evaluation of an explicitly defined piecewise linear function. By computing the inherent underlying controller structure, we also solve the equivalent of the Hamilton-Jacobi-Bellman equation for discrete-time linear constrained systems. Control based on on-line optimization has long been recognized as a superior alternative for constrained systems. The technique proposed in this paper is attractive for a wide range of practical problems where the computational complexity of on-line optimization is prohibitive. It also provides an insight into the structure underlying optimization-based controllers.

Further Information
Year:

2002
Type of Publication:

(01)Article
Supervisor:



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% Autogenerated BibTeX entry
@Article { BemEtal:2002:IFA_12,
    author={A. Bemporad and M. Morari and V. Dua and E.N. Pistikopoulos},
    title={{The Explicit Linear Quadratic Regulator for Constrained
	  Systems}},
    journal={Automatica},
    year={2002},
    volume={38},
    number={1},
    pages={3--20},
    month=jan,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=12}
}
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