How to specify an objective function with both a variable and its derivative?

Don

2014 11 4

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Dear all,

In order to minimize the energy used in the motion of a mass with aerodynamic drag, I need to specify an objective function. This objective function should contain both the displacement (x) and the velocity (xdot).

So basicly, the objective function should look like: W=(1/2)*C1*x*xdot^2-R*x

Does anyone know how to enter this into an objective function that the optimization toolbox can handle?

Thank you in advance!

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Don 2014-11-5

Thank you for your comment

The problem is that x (the distance travelled) should in the end amount to a ceertain value (for example 10 meters), but the speed (xdot) should be such that the amount of energy consumed (W) is minimal.

So now I need to tell MatLab that xdot is in fact the derivative of x, can I do that with diff(x)? Or do I need other ways? (In the documentation there was a lot of stuff about gradients and Hessians, but diff(x) and der(x) were never mentioned....)

Do you know how to do this? Thank you!

Matt J 2014-11-5

编辑：Matt J 2014-11-5

So now I need to tell MatLab that xdot is in fact the derivative of x, can I do that with diff(x)?

Possibly, but it would still be good to have an answer to my question above. What are the unknowns in W=(1/2)*C1*x*xdot^2-R*x and what are the dimensions of all the quantities C1,x,xdot, and R?

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