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Model predictive control of discrete event systems

Subject: Model predictive control of discrete event systems
Staff Mentor: B. De Schutter
Other Mentor(s): T. van den Boom
Keywords: Discrete-event and hybrid systems; Optimal and model predictive control
Description: Model predictive control (MPC) is a very popular controller design method in the process industry. An important advantage of MPC is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. In this project we consider the extension of MPC to a class of discrete event systems. Typical examples of discrete event systems are: flexible manufacturing systems, telecommunication networks, traffic control systems, multiprocessor operating systems, and logistic systems. In general models that describe the behavior of a discrete event system are nonlinear in conventional algebra. However, there is a class of discrete event systems - the max-plus-linear discrete event systems - that can be described by a model that is ``linear'' in the max-plus algebra.

Recently, we have developed an MPC framework for max-plus-linear discrete event systems. In general the resulting optimization problem is nonlinear and non-convex. However, if the control objective and the constraints depend monotonically on the outputs of the system, the MPC problem can be recast as problem with a convex feasible set. If in addition the objective function is convex, this leads to a convex optimization problem, which can be solved very efficiently.

The aim of this proposal is to further investigate several aspects of MPC max-plus-linear discrete event systems: development of efficient algorithms, further investigation of which cases lead to convex optimization problems, stability issues, inclusion of disturbances, noise and modeling errors, implementation issues (prediction, partial information, when to update), actual implementation on a practical example.

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Last modified: 14 November 2007, 12:57 UTC
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