Model predictive control for max-plus and continuous piecewise-affine systems

In this presentation, we give an overview of the work done at the Delft Center for Systems and Control in the field of model-based predictive control for max-plus linear systems and piecewise-affine systems.  Max-plus linear systems are a class of discrete-event systems the behavior of which can be described by state update equations that are linear in the (max,+) algebra. We focus on model predictive control (MPC) for such systems, where a given performance criterion is optimized over a given prediction horizon to determine the optimal control inputs. We show that - depending on the type of performance criterion and constraints - this can result in a linear programming or a mixed linear programming problem. In addition, we also present a general optimization approach for max-plus MPC based on optimistic optimization. Finally, we discuss the extension of our results to max-min-plus-scaling systems, which are equivalent to continuous piecewise-affine systems.

Bio: Bart De Schutter received the Ph.D. degree in Applied Sciences in 1996, at K.U.Leuven, Belgium. After obtaining his Ph.D. degree, he was a postdoctoral researcher at the SISTA-ESAT group of K.U.Leuven, Belgium. In 1998 he moved to the Control Lab of Delft University of Technology as an assistant professor. In 2000 he became associate professor. Currently, he is a full professor at the Delft Center for Systems and Control of Delft University of Technology in Delft, The Netherlands.

Bart De Schutter is associate editor of IEEE Transactions on Automatic Control and senior editor of the IEEE Transactions on Intelligent Transportation Systems.  His current research interests include control of discrete-event and hybrid systems, multi-agent systems, control of large-scale transportation networks with applications in freeway and urban traffic control, intelligent vehicle systems, smart grids, and water networks.