Almost every real-world control system is subject to state or input
constraints, e.g., limited valve positions. Model predictive control
(MPC) is an optimization-based controller that is capable of directly
including such constraints. In MPC, a model is used to predict the
system behavior on a finite prediction horizon. Based on these
predictions, a sequence of optimal control actions is computed in every
time step. After applying the first element of this sequence, the
optimal control problem (OCP) is solved again at the next sampling
instance for the new system state. In summary, MPC offers optimal system
performance subject to constraints but it requires to solve an OCP in
every time step.
Our research activities on MPC are threefold. First, we address
system-theoretic features that extend the applicability of MPC. We
develop, for example, novel methods to compute robust positively
invariant sets for tube-based robust MPC. Second, we provide more
efficient implementations of MPC. In this context, we study real-time
optimization based on projected gradient schemes or the alternating
direction method of multipliers (ADMM). Third, we investigate the
application of MPC in (potentially) insecure environments such as clouds
or networked systems. Here, we focus on secure implementations of MPC
using techniques from cryptography such as homomorphic encryption.
See the following list of selected publications for more details on our
research on MPC.
M. Schulze Darup, A. Redder, I. Shames, F. Farokhi, and D. Quevedo.
Towards encrypted MPC for linear constrained systems. IEEE Control
System Letters, 2(2): 195-200, 2018.
M. Schulze Darup, A. Redder, and D. Quevedo. Encrypted cloud-based MPC
for linear systems with input constraints. In: Proc. of the 6th IFAC
Conference on Nonlinear Model Predictive Control, 635-642, 2018.
M. Schulze Darup, G. Book, and P. Giselsson. Towards real-time ADMM for
linear MPC. In: Proc. of the 2019 European Control Conference, 2019.
M. Schulze Darup and D. Teichrib. Efficient computation of RPI sets for
tube-based robust MPC. In: Proc. of the 2019 European Control