Conditional piece-wise dependent regression

Hi, after reading some R docs, I couldn?t figure out how can I find the solution for the following
problem, therefore I would ask this friendly list for an advice.

We?re making a least square approximation for an experiment described by the following model:

T is the time,
Y is some measured value.

From time=0 till time=U:

Y = b + p*T

From time=U and on (some effect added):

Y = b + p*T + q*(T-U)

From time=V and on (some additional effect added):

Y = b + p*T + q*(T-U) + r*(T-V)

Measured: Yi, Ti pairs.
Wanted: b, p, q, r.
b and p are the same for all time ranges;
q is the same for time=U and on.

Thanks,
Arie.