I'm studying nonlinear control systems, especially the Pontryagin's minimum principle and its applications. Throughout my studies, the authors have always defined the control systems with state variables and output variables. However, in this article Optimal Control of an SIR Model with Delay in State and Control Variables and so many others, it doesn't seem like control systems in epidemiology has output variables equations (or at least clear ones).
Why is so? And is it possible for a nonlinear control system not to have output variables?
I have found this answer:
It is possible for a nonlinear control system not to have an explicit output variable, depending on how the system is defined and what its purpose is. In a control system, the input variable is typically the signal or information that is used to control the behavior of the system, and the output variable is the variable that is being controlled or affected by the system. However, in some control systems, the purpose may not be to directly control an output variable, but rather to achieve some other goal.
Is it correct?