Software recommendation needed for optimal control
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My subject is optimal control of PDE and I want to put optimal control problems in Matlab to be solved but I don't know how to do this. I would be grateful if you could give me some references in that direction. An example of what I want is the following one: Consider the problem: $$begin{cases} dfrac{partial{y}}{partial{t}} -Delta y(t,x_1,x_2,x_3)=u(t)cdot f(t,x_1,x_2,x_3) \ y(t,x_1,x_2,x_3)=0, forall tin [0;T], forall x=(x_1,x_2,x_3) text{with} ||x||=1 \ y(0;x_1;x_2;x_3)=g(x_1,x_2,x_3)end{cases}$$ where $f,g$ are given functions and $u:[0;infty]to [0;1]$ is a control in $L^2$ . I want to find the control $u$ that maximizez the folowing cost functional: $$I(u)=int_{0}^{T}int_{B(0;1)} |y(t,x_1,x_2,x_3)| dx dt$$ . I know that for given $u$ i can solve the PDE with matlab tools or via a free element
