The field of control has been a key driver for major societal innovations in health, mobility, energy and manufacturing. At present, technological trends push the performance requirements for future applications to extreme levels that are far beyond current control solutions. In PROACTHIS, I will bridge this scientific gap by creating a new control paradigm based on projection operators. By introducing projectors in control loops, specific signals are kept in well-chosen constraint sets inducing direct performance-enhancing benefits. I foresee that the mathematical structure of these projection-based controllers enables fundamental properties that were instrumental in the success of linear control and will be key to obtain effective design frameworks for this new class of hybrid controllers. This scientific challenge calls for leveraging powerful multi-disciplinary methodologies from Hybrid Systems, Control Engineering, Networked Systems, Learning and Mathematics. Successfully developing this new system theory will pave the way towards game-changing cutting-edge control methodologies addressing the needs of future engineering systems, thereby enabling new breakthroughs in important societal domains.