# DFG Project "Model predictive PDE control for energy efficient building operation: Economic model predictive control and time varying systems"

**start of the project: **
2016
,
**end of the project: **
2019

**contract number: **
GR 1569/16-1

**funding institution: **

DFG (Research Grants)

## project members

### principal investigator

Prof. Dr. Lars Grüne### project members

### external project members

Prof. Dr. David Angeli (Imperial College London, UK)

## aims of the project

Heating, Ventilation and Air Conditioning (HVAC) facilities form a class of control systems which have a huge potential for energy savings. In order to realize these savings, we propose to use Model Predictive Control (MPC) as an optimization based control technique. In order to obtain the accurate models needed for MPC, we intend to explicitly take into account the spatio-temporal distribution of the state variable, i.e., to use dynamic models based on Partial Differential Equations (PDEs). This proposal, which shall be carried out in close cooperation with the partner proposals by Thomas Meurer and Stefan Volkwein, aims at analyzing and designing MPC schemes for spatially distributed and time varying models, at implementing the respective algorithms, and at applying it to a joint benchmark problem. In light of the intended energy efficiency, economic MPC formulations will be in the focus of the proposal. Here "economic MPC" stands for a class of MPC algorithms in which the control objective is not the stabilization of an equilibrium or the tracking of a time varying reference trajectory. Instead, the goal is to follow an energy optimal path which is not given a priori but implicitly defined by the objective of the MPC optimization, itself. The key question in economic MPC is how to design the objective and constraints such that the iterative optimization on moving horizons yields an approximately optimal closed loop trajectory on a long, possibly infinite time horizon. To this end, in the first work package economic MPC for PDEs will be investigated in detail. Key difficult is the fact that the system dynamics evolve in an infinite dimensional state space. Our goal is to develop new methods exploiting the special stuctures of HVAC control problems. In the second work package, problems with time varying system dynamics or depending on time varying data are considered. Here, in particular, an appropriate generalization of the concept of an optimal equilibrium must be found and appropriate terminal constraints in the time varying setting shall be developed. The third work package concerns the implementation. Beyond the coding of the newly developed routines, which will be carried out in close collaboration with the partner projects, the a posteriori performance measure for stabilizing MPC shall be extended to economic MPC, as a device to measure the errors introduced by using reduced order models in the optimization. The results from all work packages will be applied and particularly focused to a benchmark problem for HVAC control. These activities are detailed in the fourth work package and will be carried out in parallel with the other work packages.

The project will be carried out in close cooperation with the DFG projects "Flatness-based MPC and observer design for PDE systems" and "Reduced-order methods for nonlinear model predictive control".

For more information visit the webpage of the project.