Optimize for multiple variables in nonlinear function

I need to optimize the charging of a battery. I have the price for power per hour; €P(i). I want to charge the battery in t_final hours. The level of the battery after every hour, L(i) is a (nonlinear) function of the power inserted, P(i) and the Level which it had before the start of that hour; L(i) = f(L(i-1),P(i)). I need to find the optimal values for P(i) that minimize SUM( €P(i)*P(i) ) while keeping L(t_final) at 1.

How can I do this?

Answer 1

[Torsten]

min: sum_{i=1}^{t_final} Power_inserted(i)*Price(i)

s.t.

L(t_final)-1=0

Unknowns are Power_inserted(i) (i=1,...,t_final).

To get L(t_final), you will have to compute L(1),...,L(t_final-1) from the unknowns Power_inserted(i).

A typical problem for MATLAB's "fmincon".

Best wishes

Torsten.