code for NLP formula in latex

There are some errors that I see in your code. Mainly, the use of subscripts inside text{}. And also some things that might look better written in a different way. This code produces something similar to your image.

begin{equation*}
T_{i} = begin{cases}
1, & text{T $leq$ 1}
1+ beta T, & text{T$>$ 1} end{cases},
text{ in which } T = 
begin{cases}
T_{now}-T_{last}, & T_{last} neq NULL 
T_{now}-T_{update}, & T_{last} = NULL
end{cases}
end{equation*}

If you need it inside the align environment, you can change of course, the begin{equation*} and end{equation*} to begin{align} and end{align}.

If you want to know a bit more why your code does or doesn't work, or about my code, just let me know.

The following code produces the result you're after. I find it best not to try to make the various components line up in your tex editor as they would on the page because adjusting the zoom ruins it anyway.

begin{document}
begin{equation}
T(i) = begin{cases} 1, T geq 11 + beta T, T > 1 
end{cases}emph{, in which } T = begin{cases}T_{now}- 
T_{last}, T_{last} neq NULLT_{now}-T_{update}, T_{last} 
neq NULLend{cases}
end{equation}
end{document}

I more prefer the following result:

which is produced by

documentclass{article}
usepackage{amsmath}

begin{document}
    [
T_{i} = begin{cases}
1       ,   & T leq 1
1+ beta T, & T > 1 
        end{cases},
text{ in which } 
T = begin{cases}
T_{mathrm{now}}-T_{mathrm{last}},   & T_{mathrm{last}} neq mathrm{NULL} 
T_{mathrm{now}}-T_{mathrm{update}}, & T_{mathrm{last}} = mathrm{NULL}
    end{cases}
    ]
end{document}