Interval Strong Solutions of Interval Systems of Max-Plus Linear Equations

https://doi.org/10.22146/jmt.66309

Fathin Azkiya(1*)

(1) Gadjah Mada University
(*) Corresponding Author

Abstract


Let R be the set of all real numbers and Rε = R ∪ {ε} whose ε = {−∞}. Max-plus algebra is the set Rε that is equipped two operations maximum and addition. Max-plus algebra can be expanded to interval max-plus algebra, it is the set of closed intervals in Rε that is equipped with the operation maximum as ⊕ and the operation addition as ⊗ . This study aims to discuss the existence and uniqueness of interval strong solutions of interval systems of interval max-plus linear equations. The proof of the existence of interval strong solutions is constructive and generates a formula for computing such solutions. A necessary and sufficient condition for the uniqueness of interval strong solutions is obtained by testing the uniqueness of the solution of a finite number of subsystems from all of its subsystems. From these conditions, an algorithmcan be obtained that can verify the uniqueness of interval strong solutions of interval systems of max-plus linear equation

Keywords


Max-plus linear equation, interval system, strong solvable, interval strong solution.

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References

Bacelli, F., Cohen, G., Olsder, G.J. dan Quadrat, J.P., Synchronization and Linearity, John Wiley and Sons, New York, 1992.

Cechl´arova, K. dan Cuninghame-Green, R.A., Interval Systems of Max-separable Linear Equations, Linear Algebra and its Application 340 (2002), 215-224.

Cuninghame-Green, R., Minimax Algebra, Springer-Verlag, New York, 1979.

Heidergott, B., Olsder, G. J. dan van der Woude, J., Max Plus at Work, Princeton University Press, New Jersey, 2006.

Wang, C. dan Tao, Y., Interval Strong Solutions of Interval Systems of Max-plus Linear Equations, Linear Algebra and its Applications, 537 (2018), 148-159.

Wang, C., Tao, Y. dan Yang, P., Reachability for Interval Max-Plus Linear Systems, Proceedings of the 36th Chinese Control Conference, (2017), 26-28.

Zhang, H., Tao, Y. dan Zhang, Z., Strong Solvability of Interval Max-plus Systems and Applications to Optimal Control, Systems and Control Letter, 96 (2016), 88-94.



DOI: https://doi.org/10.22146/jmt.66309

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