%0 Book Section
%A Borrelli, Francesco
%A Baotic, Mato
%A Bemporad, Alberto
%A Morari, Manfred
%B Conference on Decision and Contml
%D 2008
%F eprints:477
%I Society for Industrial and Applied Mathematics:3600 University City Science Center:Philadelphia, PA 19104:(800)447-7426, (215)382-9800, EMAIL: service@siam.org, INTERNET: http://www.siam.org, Fax: (215)386-7999
%K computational complexity; constrained optimal control; discrete-time linear time-invariant systems; explicit optimal control law evaluation; initial state; input constraints; model-predictive control; multi-parametric programming;online computation; open-loop constrained finite-time optimal controller; output constraints; piecewise-affine function; sampling time; storage demands; value function; computational complexity; constraint theory; control system analysis computing; mathematical programming; online operation; predictive control; time optimal control.
%P 2470-2489
%T Efficient on-line computation of constrained optimal control
%U http://eprints.imtlucca.it/477/
%V 47
%X For discrete-time linear time-invariant systems with constraints on inputs and outputs, the constrained finite-time optimal controller can be obtained explicitly as a piecewise-affine function of the initial state via multi-parametric programming. By exploiting the properties of the value function, we present two algorithms that efficiently perform the online evaluation of the explicit optimal control law both in terms of storage demands and computational complexity. The algorithms are particularly effective when used for model-predictive control (MPC) where an open-loop constrained finite-time optimal control problem has to be solved at each sampling time.