Stabilization of max-plus-linear systems using model predictive control: The unconstrained case |
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Authors: | Ion Necoara [Author Vitae] Ton J.J. van den Boom [Author Vitae]Author Vitae] Hans Hellendoorn [Author Vitae] |
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Affiliation: | Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands |
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Abstract: | Max-plus-linear (MPL) systems are a class of event-driven nonlinear dynamic systems that can be described by models that are “linear” in the max-plus algebra. In this paper we derive a solution to a finite-horizon model predictive control (MPC) problem for MPL systems where the cost is designed to provide a trade-off between minimizing the due date error and a just-in-time production. In general, MPC can deal with complex input and states constraints. However, in this paper we assume that these are not present and it is only required that the input should be a nondecreasing sequence, i.e. we consider the “unconstrained” case. Despite the fact that the controlled system is nonlinear, by employing recent results in max-plus theory we are able to provide sufficient conditions such that the MPC controller is determined analytically and moreover the stability in terms of Lyapunov and in terms of boundedness of the closed-loop system is guaranteed a priori. |
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Keywords: | Discrete-event systems Max-plus-linear systems Model predictive control Lyapunov stability Bounded buffer stability |
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