Repository including all calculations for the case study of the eponymous paper.
This paper exploits the efficient computation of reachable sets for monotone systems to formulate model predic- tive control approaches with guaranteed constraint satisfaction and recursive feasibility in the presence of uncertainty. To include all realizations of uncertain parameters, the reachable sets are approximated as hyperrectangles in the problem formulation. The presented approach is extended to include recourse, i.e., the knowledge about the presence of further measurement information in the prediction horizon. By dividing the reachable sets, multiple regions are obtained, for which the future inputs can be chosen separately. The applicability of the proposed approaches are shown by the means of a temperature control example.
Thank you for looking into the supplementary code! All the calculations presented in this paper were done in Python and can be reevaluated in the Jupyter Notebook. The main toolboxes used for this are:
- numpy
- matplotlib
- CasADi
As well as our own toolbox do-mpc.
The Jupyter Notebook is structured as follows:
First the Model with 4 Rooms is introduced and the simulator is created. Then the Uncertainties and the external influences are defined/loaded. Then a nominal MPC controller gets defined and used, which produces parts of the results from Figure 2 of the paper. The Open Loop Approach was not used in this case study, but can be evaluated to see, that it produces indeed infeasible results. The Closed Loop Approach follows next, which produces parts of the results from Figure 2 of the paper by varying the uncertainty functions. For the simplified closed Loop approach, the robust control invariant set is computed interlinked for the whole prediction horizon. These sets are then used for the simplified approach, which also produces parts of the results from Figure 2 of the paper by varying the uncertainty functions. Again the approach of computing RCIS is presented, for non-timevarying parameters. Finally the Post-Processing for Figure 2 is presented.
If some questions arise, please feel free, to contact me!