The Controller Synthesis Problem: Implementability and robustness
Youssouf Oualhadj · HAL (Le Centre pour la Communication Scientifique Directe) · 2024
The controller synthesis problem lays the ground for a formal toolbox allowing a “correctby design” paradigm. Nevertheless bringing the theory and application together implies at theleast the possibility of a realistic physical implementation of the designed controller. However,one has to keep in mind that this controller is nothing but a mathematical idealization of acorrect solution in where (some) physical constraints are often abstracted away. For instance,the obtained controller does not have memory constraint, nor it is concerned with energyconsumption, or hardware limitation such as clock speed. Sometimes, the time guaranteesbrought by the computed solution are simply not realistic. For example, in the case where aspecificationrequiresrepeatedbehavior, acontrollerinducingabehaviorwhereeachrepetitionrequires arbitrary longer period of time to take place is deemed correct. In this case, thecontroller can be implemented but its behavior is still not completely satisfying. This comesfrom the fact that usually the specification formalism used allows, from a mathematical standpoint, such behaviors. One can obviously say it suffices to use a more precise specification,i.e., a language where such phenomena are ruled out. It turns out that this is not a simpletask. Indeed, one has to bear in mind that we are aiming for an automatic procedure, thusdecidability (and tractability) is paramount. Therefore, fine tuning the specification languagewhile maintaining algorithmic properties is an ongoing challenge.In this manuscript we present several contributions that fall in the scope of automaticallydesigned implementable controllers.