I am considering using Julia and JuMP for my Master Thesis in learning based robust economic Model Predictive Control. I hope to get some feedback from the community on what packages to use or on what functionalities are still missing, where I could possibly help contributing to julia.
In principle, implementing an MPC Controller means solving a constraint finite horizon Optimal Control Problem repeatedly. Additionally, it is important to be able to calculate invariant sets, i.e. computing the Minkowski Sum of two sets repeatedly (e.g. the sum of polyhedral and an ellipsoidal set).
At my University, we have a Matlab heavy control lab, and therefore we are also using Matlab for MPC. Specifically the Yalmip toolbox (for optimization) and the Multi-Parametric Toolbox (https://www.mpt3.org/) for the set calculations. I’d like to replace these toolboxes and Matlab by a Julia framework.
From my experience, with JuMP I should be able to define and solve the optimization problems. But for the set manipulations, I haven’t found any packages suitable for my needs.
So I was wondering, if there is already some work done on MPC in general and invariant set calculation in special or if there are plans to do so. Or if there are general caveats on using JuMP for MPC?