| Max-plus algebra is a suitable algebraic setting to model discrete event systems involving synchronization and delay phenomena which are often found in transportation networks, communications systems and manufacturing systems. One way of controlling this kind of systems consists in choosing the dates of input events in order to achieve the desired performances, e.g., to obtain output events in order to respect given dates. This kind of control is optimal, according to a just-in-time criterion, if the input-event dates are delayed as much as possible while ensuring the output events to occur before a desired reference date. This thesis presents the observer-based controller for max-plus linear systems where only estimations of system states are available for the controller, which is solved in two steps: first, an observer computes an estimation of the state by using the input and the output measurements, then, this estimated state is used to compute the state-feedback control action. It is shown that the optimal solution of this observer-based control problem leads to a greater control input than the one obtained with the output feedback strategy. Moreover, for the uncertain max-plus linear systems have varying processing time between each transition, this thesis presents robust observer-based controller towards optimizing process scheduling of a timed event systems according to the just in time criterion. Applications of the main results are illustrated in a high throughput screening system in drug discovery and a transportation network. |
