MSc projects

The aim of this project is to develop systematic and general design procedures that can be used to develop non-linear model predictive controllers based on linear-parameter varying (LPV) embeddings. Recently, we proposed a tube-based MPC scheme which can be used to control non-linear systems represented in terms of an LPV embedding. Based on artificially constructed state constraints, a sequence of sets is generated which contains all possible future trajectories of the scheduling variable which captures the non-linearities of the process. This method has been shown to work in principle, but as of yet we do not have a general approach to design the artificial state constraints or to generate the sets describing all possible trajectories of the scheduling variable. Such approaches will be developed in this project. Furthermore, it is also of interest to implement and study the performance of the controller on examples from the literature, in order to gain more insight in its performance and limitations when compared to full non-linear MPC. Background Many systems in engineering exhibit significant non-linearities when controlled over a wide operating regime. Because working with complex non-linear models is challenging, it is often useful to employ “simplifying” approaches to model the non-linear system. These simplifications can be used to re-cast the control problem in a setting where it can be efficiently solved, with an acceptable trade-off in terms of the achievable performance. One such way of modeling the behavior of a non-linear system is by embedding it in a linear parameter-varying (LPV) representation. In an LPV system, the dynamical mapping between inputs and outputs is linear while the mapping itself depends on a time-varying and on-line measurable scheduling variable. Thus, non-linearities in the original system can be represented by variations in the scheduling signal.