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Optimal input design for uncertain max‐plus linear systems
Author(s) -
Wang Cailu,
Tao Yuegang,
Yan Huaicheng
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4285
Subject(s) - interval (graph theory) , mathematics , control theory (sociology) , optimal control , range (aeronautics) , set (abstract data type) , optimal design , mathematical optimization , linear system , linear programming , computer science , control (management) , statistics , engineering , combinatorics , artificial intelligence , programming language , aerospace engineering , mathematical analysis
Summary 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.