hi guys, I have a mathematical expression here, could someone identify the name of the topic it falls under, or if someone is familiar with this expression (any keyword?) could you tell me what exactly it is?

Here Ht is a state variable. Guys who familiar with optimization problem should well know that it is usually assumed the state variable is continuous and smooth, e.g., the motion of capital in the optimal growth model. However, I want to assume the state Ht response to control variable Rt conditionally. I want to search in google whether others have such an assumption in their academic paper but I did not know what is the 'exact expression' of this 'conditional motion'. I tried "nonsmooth motion of state variable", "kinked state variable" but it seems those expressions are not accurate.

Any suggestion and help is appreciated. Thank you.