Abstract
We consider the control of a class of convolution systems subject to constraints on the state and the control, using the search of invariant sets. Our motivations come from production management. The papers provides an explicit characterization of the \(\mathscr {D}\)-invariance property of polytope sets for continuous-time systems. An interesting application of the concept of \(\mathscr {D}\)-invariance is to investigate the possibility of controlling a class of convolution system. The considered system corresponds to a supply chain. The controller design problem for supply chain, with constrained orders and inventories, and unknown customer demands variations, has been investigated. The problem is stated in terms of controlled input time delay system, with positivity constraints, subject to bounded disturbances.
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Bou Farraa, B., Abbou, R., Jacques Loiseau, J. (2022). Control by Set Invariance of a Class of Convolution Systems. In: Valmorbida, G., Michiels, W., Pepe, P. (eds) Accounting for Constraints in Delay Systems. Advances in Delays and Dynamics, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-89014-8_3
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DOI: https://doi.org/10.1007/978-3-030-89014-8_3
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