Model Matching Problems for Max-plus Linear Systems with Polytopic Uncertainty in the Dynamics

This work deals with the problem of finding a control input that forces the output of a max-plus linear system, affected by polytopic uncertainty in the dynamics, to match the output of a given model. Model matching is a fundamental problem in control theory and its solution provides a powerful and viable control strategy in many situations. Polytopic uncertainty arises naturally in modeling real plants whenever their parameters are only known to belong to given intervals of values. The approach to the model matching problems adopted herein leverages structural notions derived from the geometric approach to systems with coefficients in a field and exploits interpretations grounded on max-plus algebraic theory. Novel notions, such as robust controlled invariance and robust feedback controlled invariance, are specifically defined for uncertain max-plus linear systems and used to derive constructive, sufficient, solvability conditions for the stated problems. The methodological discussion ends with an illustrative example aimed to show feasibility and effectiveness of the proposed approach.