# Optimal control problem

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
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On Tue, 14 Aug 2007 02:30:37 +0800, Everett X. Wang wrote:

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.
--
Tim Wescott
Control systems and communications consulting
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wrote:

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
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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

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On Thu, 16 Aug 2007 06:37:53 -0700, "Boen S. Liong"

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