%0 Book Section
%A Bemporad, Alberto
%A Filippi, Carlo
%B Decision and Control Conference
%C Orlando, Florida USA, December 2001
%D 2001
%F eprints:586
%I IEEE
%K approximate multiparametric quadratic programming; approximate solutions; degree of approximation; discrete-time linear time invariant system; linear constraints; optimization problem; parameter space; piecewise affine function; polyhedral cells; suboptimal explicit model predictive control; discrete time systems; linear systems; predictive control; quadratic programming; vectors
%P 4851-4856
%T Suboptimal explicit MPC via approximate multiparametric quadratic programming
%U http://eprints.imtlucca.it/586/
%V 5
%X Algorithms for solving multiparametric quadratic programming (mp-QP) were proposed in Bemporad et al. (2001) and Tondel et al. (2001) for computing explicit model predictive control (MPC) laws. The reason for this interest is that the solution to mp-QP is a piecewise affine function of the state vector and thus it is easily implementable on-line. The main drawback of solving mp-QP exactly is that whenever the number of linear constraints involved in the optimization problem increases, the number of polyhedral cells in the piecewise affine partition of the parameter space may increase exponentially. We address the problem of finding approximate solutions to mp-QP, where the degree of approximation is arbitrary and allows a trade off between optimality and a smaller number of cells in the piecewise affine solution