Optimal control problem

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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?

Thanks in advance,

Everett

 

Re: Optimal control problem



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
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

Re: Optimal control problem



wrote:


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

Thanks a lot.

Everett

Re: Optimal control problem



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






Re: Optimal control problem



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



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