Strong solvability of interval max-plus systems and applications to optimal control

This paper considers the strong solvability of interval max-plus systems. The solvable entry and solvable interval are introduced to establish the necessary and sufficient condition for strong solvability of interval max-plus systems. It is proved that such a criterion is equivalent to the criterion proposed by Cechlárová and Cuninghame-Green. The interval strong solution of interval max-plus systems is described and the necessary and sufficient condition for uniquely strong solvability is given. The method of testing strong solvability of interval max-plus systems is constructive and leads to an effective algorithm. To illustrate our results, a workshop optimal control problem is addressed.