Optimal input design for uncertain max-plus linear systems

This paper investigates the optimal input design for uncertain max-plus linear systems whose parameters are only known to belong to certain intervals. The exact interval input is introduced to minimize the regulating range of the input that ensures that the system can output at any specified value in the desired interval regardless of how the parameters vary in certain ranges. The optimal input design for uncertain max-plus linear systems is formulated as an optimal control problem that finds the maximum element of the set of exact interval inputs with respect to the order of max-plus interval vectors. This paper also considers the optimal approximate interval input of an uncertain max-plus linear system that has no exact interval input. A polynomial algorithm is developed to find the optimal interval input and optimal approximate interval input of an uncertain max-plus linear system. A data transmission system with parameter perturbations is employed as an example to demonstrate how the proposed results work in practical applications.