From monotone inequalities to Model Predictive Control

The dater equalities constitute a well-known tool which allows the description of timed event graphs in the field of (max, +) algebra. This paper gives an equivalent model in the standard algebra which can describe timed event graphs with inputs and outputs. Concepts of componentwise order and monotone inequalities prove the existence of unique minimum, or maximum, solution in special system Ax les b. The approach is applied to just in time control and model predictive control. Connections with linear programming are made.