This paper addresses the problem of dynamic input allocation for nonlinear systems that exhibit a redundant input configuration and admit a periodic steady-state behavior. The control task is formulated in a general framework that encompasses a wide variety of practical scenarios, providing greater flexibility in the definition of the operators involved. The peculiar challenges posed by nonlinear control allocation problems are then examined from a different perspective, offered by a formulation in the context of optimal control theory. The similarities and differences between the two formulations are highlighted and discussed, with the aim of establishing a link between the two subjects in order to share their respective tools and results. Finally, an algorithm to determine approximate solutions to the control allocation problem is developed and refined using dynamic optimization tools.

This work addresses the input current allocation problem for the magnetic control system of the Tokamak à Configuration Variable (TCV). Given the available actuators (i.e. poloidal field coils) on the TCV device, this work aims to optimize the input current configuration concerning a desired cost function, minimizing the effect on the controlled output, which is, in this case, considered as the plasma shape. This request is formulated as a dynamic control allocation problem, and a solution is proposed, discussed, and validated by numerical simulations on TCV models and data.