[Ipopt] about state variable and control variable in IPOPT

Christian Wolf ChristianLupus at gmx.de
Wed Oct 29 06:13:18 EDT 2014

```Hello,

in fact you are describiing here the "direct approach" for solving
optimal control problems.
I did similar things using ipopt a few years ago.

If you try to only optimize over the inputs u only, you might get into
trouble if the underlying system is not behaving "well" (for example is
unstable.
Nevertheless you could do it and use for example the sensitivity
differential equation to calculate the derivatives.

In any case (to make this clear) you have to discretize the time in any
fashion.
Then the control input u is kept constant in each time slice.

There might be better solutions (of higher degree) available, but this
depends on the knowledge of the thread starter if those are applicable.

Hope this helps
Christian
Am 28.10.2014 um 08:45 schrieb Tony Kelman:
> You can do either approach. If you have a long time horizon or
> complicated state constraints it might be beneficial to include both
> state and input variables in your optimization variable vector, and
> enforce your system dynamics as equality constraints. So z = [x; u],
> and you want to minimize f(z) s.t. g(z) = 0, h(z) <= 0. In this form
> the Jacobian of g and h would depend on both x and u. Depending on
> your problem structure, it's often better to let Ipopt handle solving
> equality constraints for you, rather than trying to do anything too
> clever with solving for x as a function of u at every iteration, which
>
>
> -----Original Message----- From: Philipp Bender
> Sent: Tuesday, October 28, 2014 12:23 AM
> To: ipopt at list.coin-or.org
> Subject: Re: [Ipopt] about state variable and control variable in IPOPT
>
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> Hello Kayan,
>
> so you want to solve an optimal control problem with IpOpt?
>
> Like: what is the best action u, given state x? (Maximize expected
> reward or some such?)
>
> I don't know if your approach is feasible at all, but if you intend
> what I stated above, I think you should not make x part of your
> optimization parameters, since you are interested in u. Then you have
> a "normal" optimization problem, but with properties I am not aware of.
>
> Best regards,
> Philipp
>
> - -- Dipl.-Ing. Philipp Bender
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```