# Optimal control problem

• posted

Hi All,

I am working on a mobile robot project, using optimal control. I know how to obtain Euler-Lagrange equations for a system with dynamic equation in the form:

dx/dt = f(x,u), where x is the state vector, u is the control

Now if my dynamic equation has the form of

dx/dt = f(x,u, u', u''), where u' = du/dt and u'' = d^u/dt^2.

Can this type of problem be solved by optimal control? What are the equivalent Euler-Lagrange equations?

Everett

• posted

I couldn't tell you the equivalent Euler-Lagrange equations, but consider a system defined as dx_a/dt = f_a(x_a, u_a), where u_a = u'', x is augmented with u' and u, and f_a is modified appropriately so that u' is the integral of u'' and u is the integral of u'.

Then you should just be able to analyze this with the tools you have, maybe.

• posted

Hi Tim,

This is a great idea. It will work. I looked several optimal control books and haven't seen this trick.

Thanks a lot.

Everett

• posted

Hi Mr. Wang and Mr. Tim Wescott,

Incidentally, I am interested in building a robot. May I know whta kind of robot are currently working on? Is this a robot that has vision, limbs, heads and stomach like a human being? Or is it just a moving robot of any shape?

Thank you,

Boen S. Liong

• posted

I can't comment on other people's project. But my robot is a "simple" one that it doesn't have head or limbs, no vision nor stomach. But it is very complex for me already.

Everett

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