Date of Award
Doctor of Philosophy
Discrete event systems (DES) are a special class of dynamical systems with discrete-valued state space and event-driven transitions. DES are ubiquitous in today's world and are used in different sectors such as manufacturing systems, transport networks and computer networks. They offer unique capabilities, such as flexibility and adaptability; at the same time, they can be challenging to model and analyze. Moreover, the complexity of DES is scaled up when disturbances are present. Many different kinds of real life DES can be modeled using dioid algebra which is a powerful tool for describing nonlinear behaviors using linear system models. Dioid algebra is an exotic algebra of formal series which can be understood as a set of only positive numbers without negatives. This special algebraic structure is useful in modeling DES because such systems feature variables that cannot be inverted with respect to some variables. Nonlinear behaviors of DES are able to be modeled as linear systems in terms of dioid algebra in order to use classical control techniques in scheduling and control of DES.This dissertation presents the scheduling and control of DES using a special dioid called max-plus algebra, which is a set of real numbers with the operation of maximum and addition replacing the usual classical operations of addition and multiplication, respectively. This dissertation also studies the behavior of DES when disturbances are present. Two different paths to the scheduling of DES are presented: using dioid algebra and using linear programming methods. The control of DES with disturbances and uncertainties is also explored, particularly, the solutions of the disturbance decoupling problem and the modified disturbance decoupling problem using various controller structures are presented. Disturbance decoupling in this dissertation means the scheduling of the DES will not not be affected by the presence of the disturbances. On the other hand, modified disturbance decoupling means the scheduling will not be worse than the delays caused by the disturbances in industrial just-in-time (JIT) standards. JIT means that the operations start with just enough time to be completed by the desired schedule in order to minimize waste and costs in work in progress and material storage.The applicability of the approach presented in this dissertation is demonstrated in real-world processes including a large-scale high throughput screening (HTS) system in drug discovery and an optimal scheduler for an airport's runways. The main contributions of this dissertation are max-plus and mathematical programming solutions for scheduling and control of discrete event systems with disturbances. The results present a theoretical scheduling prior to exhaustive scheduling algorithms in large-scaled industrial systems.
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