Value function iteration with habit

I would like to know how I could write a value function when there are habits in preferences. I have the following equations:

$$
uleft(C, t, H_{t}, L_{t}right)=frac{left(C_{t} / H_{t}^{kappa}right)^{1-gamma}}{1-gamma}-theta frac{L_{t}^{1+1 / chi}}{1+1 / chi}
$$
Habits are external in the sense that they depend on past aggregate consumption, so from the perspective of atomistic households, they are exogenous.
$$H_{t}=C_{t-1}
$$

Resource constraint gives: $Y_t=C_t+ I_t=C_t +K_t-(1-delta) K_{t-1}$. There is technology $Z_t$ following a standart AR(1) process.

How should I write the policy functions in Matlab’s code? Should I write them as 2 dimensional, that is to say, they would depend only on the grid of capital and the grid of technology? Or should they be 3 dimensional, namely they would depend on the grid of capital, the grid of technology, and the grid of $H_t$ ?

Thank you