# Differential Equations (Control Optimization Problem)

• A
• Alexandru999
Alexandru999
TL;DR Summary
Differential Equations

y_{1}{}'=y_1{}+y_{2}

y_{2}{}'=y_2{}+u

build a control

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

for the care of the appropriate system solution

y_{1}(0)=y_{2}(0)=0

satisfy
y_{1}(1)=1 ,y_{2}(1)=0

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?

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Mentor
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

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

Requirement

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

HELP !

for the system
above