Software recommendation needed for optimal control












0














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 method (with FreeFem), but I do not see how write this problem in Matlab or other softwares. Any reference would be very appreciated by me. My goal is to simulate in a software the problems that I study in optimal control PDE.



Is there a software that solves numerically optimal control problems, even for ODE?



Thanks!






math-software optimal-control







share|cite|improve this question
























  • If you want to 'write this problem in MatLab' then you could use the PDE toolbox uk.mathworks.com/help/pde/ug/equations-you-can-solve.html
    – Eddy
    13 hours ago
















0














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 method (with FreeFem), but I do not see how write this problem in Matlab or other softwares. Any reference would be very appreciated by me. My goal is to simulate in a software the problems that I study in optimal control PDE.



Is there a software that solves numerically optimal control problems, even for ODE?



Thanks!






math-software optimal-control







share|cite|improve this question
























  • If you want to 'write this problem in MatLab' then you could use the PDE toolbox uk.mathworks.com/help/pde/ug/equations-you-can-solve.html
    – Eddy
    13 hours ago














0












0








0







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 method (with FreeFem), but I do not see how write this problem in Matlab or other softwares. Any reference would be very appreciated by me. My goal is to simulate in a software the problems that I study in optimal control PDE.



Is there a software that solves numerically optimal control problems, even for ODE?



Thanks!






math-software optimal-control







share|cite|improve this question















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 method (with FreeFem), but I do not see how write this problem in Matlab or other softwares. Any reference would be very appreciated by me. My goal is to simulate in a software the problems that I study in optimal control PDE.



Is there a software that solves numerically optimal control problems, even for ODE?



Thanks!






math-software optimal-control




math-software optimal-control






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 days ago

























asked 2 days ago









Bogdan

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  • If you want to 'write this problem in MatLab' then you could use the PDE toolbox uk.mathworks.com/help/pde/ug/equations-you-can-solve.html
    – Eddy
    13 hours ago


















  • If you want to 'write this problem in MatLab' then you could use the PDE toolbox uk.mathworks.com/help/pde/ug/equations-you-can-solve.html
    – Eddy
    13 hours ago
















If you want to 'write this problem in MatLab' then you could use the PDE toolbox uk.mathworks.com/help/pde/ug/equations-you-can-solve.html
– Eddy
13 hours ago




If you want to 'write this problem in MatLab' then you could use the PDE toolbox uk.mathworks.com/help/pde/ug/equations-you-can-solve.html
– Eddy
13 hours ago










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