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The Explicit Solution of Model Predictive Control via Multiparametric Quadratic Programming


A. Bemporad, M. Morari, V. Dua, E.N. Pistikopoulos

American Control Conference, Chicago, USA, vol. 2, pp. 872-876

Control based on on-line optimization, popularly known as model predictive control (MPC), has long been recognized as the winning alternative for constrained systems. The main limitation of MPC is, however, its on-line computational complexity. 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 associated with MPC, and show that it is piecewise linear and continuous. The controller inherits all the stability and performance properties of MPC, but the on-line computation is reduced to a simple linear function evaluation instead of the expensive quadratic program. The new technique is expected to enlarge the scope of applicability of MPC to small-size/fast-sampling applications which cannot be covered satisfactorily with anti-windup schemes. A correction note for this paper can be found here:

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% Autogenerated BibTeX entry
@InProceedings { BemEtal:2000:IFA_673,
    author={A. Bemporad and M. Morari and V. Dua and E.N. Pistikopoulos},
    title={{The Explicit Solution of Model Predictive Control via
	  Multiparametric Quadratic Programming}},
    booktitle={American Control Conference},
    address={Chicago, USA},
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