Extension of the theory of monotone systems to cope with transmission delays. Adaptation of the predictive control design.

Monotony and non-negativity play a key role in understanding many processes and related physical constraints in biological and medical sciences as well as various engineering areas. Roughly speaking, the corresponding models are composed of homogeneous in terconnected subsystems which exchange variable nonnegative quantities of material with conservation laws describing transfer, accumulation, and outflows between compartments and the environment subject to appropriate partial order relations. A key physic al limitation of such systems is that transfer between subsystems is not instantaneous, and realistic models for capturing the dynamics of such systems should account for material, energy, or information in transit between compartments, and delay models c an be used to represent such dynamical behaviours. Hence, to accurately describe the evolution of compartmental systems, it is necessary to include in any mathematical model of the system dynamics some information about the past system states. This of cou rse leads to (infinite-dimensional) delay dynamical systems. The aim of this project is to better understand the effects induced by the presence of delays on the corresponding dynamics and to use Model Predictive Control (MPC) as control strategy to accou nt for the operational and structural constraints in this framework. The first objective is to fill in the gap between monotone systems and systems with delay, to designing a comprehensive theory of cooperative nonlinear systems with delays and in partic ular to the nonnegative systems. Second, we will focus on nonlinear systems which can be stabilized by control laws with delay and adapt the prediction mechanisms to this class of dynamics. Our last objective will be the extension of the results obtain ed for time-delay systems to the specific class of hybrid systems called NCS systems (Networked Control Systems).