Hamiltonian (control theory)
A Hamiltonian is like a magic number that tells us how things are going to change over time. Imagine you are playing with a toy car, and you want it to move in a specific way. You can use a Hamiltonian to tell the car what to do!
Now, let's pretend that the Hamiltonian is a special recipe that gives the car instructions on how to move. It tells the car what to do based on the starting point, where it wants to end up, and the things that might get in the way (like a wall or other toys).
In control theory, Hamiltonians are used to control things like robots or planes. You can think of the Hamiltonian as the brain of the robot or plane, telling it what to do and how to do it. Just like a recipe, the Hamiltonian helps the robot or plane figure out the best way to move and get to where it needs to go.
So, in summary, a Hamiltonian is like a special recipe or brain that helps control things like robots or planes, telling them how to move and what to do to achieve their goals.
Now, let's pretend that the Hamiltonian is a special recipe that gives the car instructions on how to move. It tells the car what to do based on the starting point, where it wants to end up, and the things that might get in the way (like a wall or other toys).
In control theory, Hamiltonians are used to control things like robots or planes. You can think of the Hamiltonian as the brain of the robot or plane, telling it what to do and how to do it. Just like a recipe, the Hamiltonian helps the robot or plane figure out the best way to move and get to where it needs to go.
So, in summary, a Hamiltonian is like a special recipe or brain that helps control things like robots or planes, telling them how to move and what to do to achieve their goals.