Reference:
B. De Schutter,
W.P.M.H. Heemels, and
A. Bemporad,
"Max-plus-algebraic problems and the extended linear complementarity
problem - Algorithmic aspects," Proceedings of the 15th IFAC World
Congress (b'02), Barcelona, Spain, pp. 151-156, July 2002.
Abstract:
Many fundamental problems in the max-plus-algebraic system theory for
discrete event systems - among which the minimal state space
realization problem - can be solved using an Extended Linear
Complementarity Problem (ELCP). We present some new, more efficient
methods to solve the ELCP. We show that an ELCP with a bounded
feasible set can be recast as a standard Linear Complementarity
Problem (LCP). Our proof results in three possible numerical solution
methods for a given ELCP: regular ELCP algorithms, mixed integer
linear programming algorithms, and regular LCP algorithms. We also
apply these three methods to a basic max-plus-algebraic benchmark
problem.