Differential Equations (Control Optimization Problem)

In summary, we are looking for a control u that will lead to a solution satisfying the given initial and final conditions for a system described by two differential equations. The control model to be used is not specified.
  • #1
Alexandru999
3
0
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 ControlHELP! i need to find control u

I am not cost functional, how to solve?
 
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  • #2
Welcome to the PF. :smile:

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.?
 
  • #3
berkeman said:
Welcome to the PF. :smile:

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.?

RequirementBuild 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
 

Related to Differential Equations (Control Optimization Problem)

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model the behavior of systems that change over time, such as motion, growth, and decay.

2. What is a control optimization problem?

A control optimization problem is a type of mathematical optimization problem that involves finding the optimal control inputs for a system in order to achieve a desired outcome. It is often used in engineering and economics to maximize or minimize a specific objective while satisfying constraints.

3. How are differential equations used in control optimization problems?

Differential equations are used in control optimization problems to model the behavior of a system and its response to different control inputs. These equations are then used to formulate the optimization problem and find the optimal control inputs that will achieve the desired outcome.

4. What are some common techniques used to solve control optimization problems?

Some common techniques used to solve control optimization problems include calculus of variations, dynamic programming, and Pontryagin's maximum principle. Other methods such as gradient descent and genetic algorithms can also be used.

5. What are some real-world applications of control optimization problems?

Control optimization problems have a wide range of applications in various fields, including robotics, economics, and aerospace engineering. Examples include designing optimal control strategies for autonomous vehicles, finding the best investment portfolio, and optimizing the trajectory of a spacecraft.

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