# Talk:Optimal control

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Field: Analysis

## Emphasis on Pontyargin

I believe that this gives too much emphasis on Pontyargin. the work of the Univ of Chicago folks on variational calculas was most important. Pontryagin results were more powerful and elegant and displaced these earlier results but most of the work of the 50's was done with the Univ of Chicago foundation.Mangogirl2 03:19, 9 July 2007 (UTC)

The main reason for underlining matrixes (as per comment by User:Oleg_Alexandrov), in mathematics and engineering, is to differentiate them from scalars or vectors. Sure, capital letters can also be used; I am sorry I didn't check for consitency first.

Underlining matrices is in fact rather rare in mathematics, as can be seen by a quick look at various Wikipedia articles on mathematical topics. I can think of only two specific situations where it is occasionally done: in fluid mechanics (where tensors are doubly underlined) and in hand-written or badly type-set text, where one cannot use boldface. I'm therefore against underlining matrices in this article.
Personally, I think it looks ugly and it is rather useless, since the reader needs to remember what all the variables stand for anyway. For the same reasons, I am against using boldface for vectors, but I know that this is more controversial. -- Jitse Niesen 11:59, 9 Jun 2005 (UTC)
Agree with Jitse. I wish to thank the anonimous contributior for the explanation. Oleg Alexandrov 16:34, 9 Jun 2005 (UTC)
I am accustomed to vectors written in bold lower case, and matrices in bold upper case. Underlining is alien to my visual understanding.132.181.160.42 01:15, 3 May 2007 (UTC)

## Comparison to dynamic programming

I was looking through a working paper introduction to dynamic programming [1] and saw the following: "Dynamic programming has strong similarities with optimal control, a competing approach to dynamic optimization. Dynamic programming has its roots in the work of Bellman (1957), while optimal control techniques rest on the work of the Russian mathematician Pontryagin and his coworkers in the late 1950s. While both dynamic programming and optimal control can be applied to discrete time and continuous time problems, most current applications in economics appear to favor dynamic programming for discrete time problems and optimal control for continuous time problems." Is this an accurate portrayal of how these are used? Should we link the two articles? Smmurphy(Talk) 18:45, 16 April 2007 (UTC)

It's not my field, but your quote matches with my limited experience and I think the articles should definitely be linked. -- Jitse Niesen (talk) 02:39, 17 April 2007 (UTC)
I am a professional economist and in my discipline, optimal control was always applied to continuous time problems. (I use the past tense deliberately; optimal control has largely fallen out of favor in economics except when expositing the Ramsey model and in Martin Weitzman's 2002 monograph.) Dynamic programming is always applied to discrete time problems, but I know of no economic problem that cannot be fruitfully explored in discrete time. Discrete time results in very little loss of generality, and grants access to a powerful body of computational techniques.132.181.160.42 01:15, 3 May 2007 (UTC)
The way I see it, the term optimal control can be used in both continuous and discrete time contexts. The term dynamic programming refers to a class problems of which discrete-time optimal control is a subset. The discrete-time equivalent to the HJB equation is the Bellman equation which is a dynamic programming. --PeR 09:39, 24 July 2007 (UTC)

## Recent reverts - Wikipedia is not a directory

I agree that a list of researchers working in the area of optimal control does not seem to be appropriate for Wikipedia. I have copied the list of researchers that was on in the article to User:DonkeyKong64/Optimal Control Researchers. Please feel free to continue adding to it from there ... for the time being.

I've been thinking about proposing a new WikiMedia project centered around academia and orgininal research. A list of researchers like the one we are discussing would be appropriate for that kind of project. Take a look at Meta:User:DonkeyKong64 if you're interested, and please post on my talk page either here or on Meta if you think this is a good idea. I haven't really fleshed the idea out much yet, but hopefully I will get a chance to some time soon. - DonkeyKong64 (Mathematician in training) 18:44, 24 July 2007 (UTC)

## Bolza, Meyer, Lagrangian

Do you think it would be fruitful to mention the three types of problems and how they are mathematically equivalent? MATThematical (talk) 20:44, 14 February 2010 (UTC)

@MATThematical Agree. Giving some examples is even better. Lbertolotti (talk) 14:11, 13 August 2015 (UTC)

## Picture

I think having a cybernetic diagram ilustrating optimal control would be nice. --Lbertolotti (talk) 14:36, 21 February 2013 (UTC)

## What's wrong with Optimal Control and how practical is it?

One problem with Optimal Control is that the continuous time cost functional, J, does not involve stability criteria. J does not involve the gain margin, phase margin, or any other stability criterion. It is not at all clear how stability criterion can be specified with J. It is quite possible that a system could perform quite well and minimize J with nominal values of model parameters. But with changes in things such as aerodynamic coefficients or parts due to manufacturing tolerances, the system could become unstable if the gain or phase margins are small in magnitude.

Quite often the best design for a system is to make it have the fastest response compatible with adequate gain and phase margins. This can be down with frequency domain criteria for optimal performance but it cannot be done with time domain performance criteria such as minimizing J. RHB100 (talk) 05:47, 14 January 2016 (UTC)