Abstract
Model predictive control (MPC) is a widely used control design method in the process industry. Its main advantage is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. We extend MPC to max-min-plus discrete event systems. In general the resulting optimization problems are nonlinear and nonconvex. However, if the state equations are decoupled and if the control objective and the constraints depend monotonically on the states and outputs of system, the max-min-plus-algebraic 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baccelli, F., Cohen, G., Olsder, G., and Quadrat, J. (1992). Synchronization and Linearity. John Wiley & Sons, New York.
Clarke, D., Mohtadi, C, and Tuffs, P. (1987). Generalized predictive control-Part I. The basic algorithm. Automatica, 23(2):137–148.
De Schutter, B. and De Moor, B. (1995). The extended linear complementarity problem. Mathematical Programming, 71(3):289–325.
De Schutter, B. and van den Boom, T. (1999). Model predictive control for max-plus-linear discrete event systems. Tech. rep. bds:99-10, Control Lab, Fac. ITS, Delft University of Technology, Delft, The Netherlands
Garcia, C., Prett, D., and Morari, M. (1989). Model predictive control: Theory and practice — A survey. Automatica, 25(3):335–348.
Gunawardena, J. (1994). Cycle times and fixed points of min-max functions. In Cohen, G. and Quadrat, J., editors, Proceedings of the 11th International Conference on Analysis and Optimization of Systems (Sophia-Antipolis, France, June 1994), volume 199 of Lecture Notes in Control and Information Sciences, pages 266–272. Springer-Verlag: London.
Jean-Marie, A. and Olsder, G. (1996). Analysis of stochastic min-max systems: Results and conjectures. Mathematical and Computer Modelling, 23(11/12):175–189.
Olsder, G. (1994). On structural properties of min-max systems. In Cohen, G. and Quadrat, J., editors, Proceedings of the 11th International Conference on Analysis and Optimization of Systems (Sophia-Antipolis, France, June 1994), volume 199 of Lecture Notes in Control and Information Sciences, pages 237–246. Springer-Verlag: London.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
De Schutter, B., van den Boom, T. (2000). Model Predictive Control for Max-Min-Plus Systems. In: Boel, R., Stremersch, G. (eds) Discrete Event Systems. The Springer International Series in Engineering and Computer Science, vol 569. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4493-7_20
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4493-7_20
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7025-3
Online ISBN: 978-1-4615-4493-7
eBook Packages: Springer Book Archive