Differential Equations (Control Optimization Problem)

[Alexandru999]

TL;DR Summary

Differential Equations

\begin{equation}
y_{1}{}'=y_1{}+y_{2}

\end{equation}

\begin{equation}
y_{2}{}'=y_2{}+u
\end{equation}

build a control
\begin{equation}

u \epsilon L^{2} (0,1)
\end{equation}




for the care of the appropriate system solution
\begin{equation}
y_{1}(0)=y_{2}(0)=0
\end{equation}


satisfy \begin{equation}
y_{1}(1)=1 ,y_{2}(1)=0
\end{equation}
Please kindly if you can help me
Discipline is Optimal Control


HELP! i need to find control u




I am not cost functional, how to solve?

 

[berkeman]

Welcome to the PF.

Schoolwork questions generally go in the Homework Help forums, but this is a complex enough question that it can probably stay here in the DE forum for now. You mentioned in our PM discussion that this is for a Master's degree level control class. Here are two of the links we were discussing as background:

https://en.wikipedia.org/wiki/Optimal_control

https://math.berkeley.edu/~evans/control.course.pdf

Can you give any more information about this question? What kind of control model are you expecting? Bang-bang, quadratic, etc.?

 

[Alexandru999]

Welcome to the PF.

Schoolwork questions generally go in the Homework Help forums, but this is a complex enough question that it can probably stay here in the DE forum for now. You mentioned in our PM discussion that this is for a Master's degree level control class. Here are two of the links we were discussing as background:

https://en.wikipedia.org/wiki/Optimal_control

https://math.berkeley.edu/~evans/control.course.pdf

Can you give any more information about this question? What kind of control model are you expecting? Bang-bang, quadratic, etc.?

Requirement


Build a control u for which The solution corresponding to a system with \begin{equation}
y_{1}(0)=y_{2}(0)=0
\end{equation} satisfy \begin{equation}
y_{1}(1)=1 ,y_{2}(1)=0
\end{equation}


HELP !



for the system
above