Talk:Hamiltonian (control theory)

Maximum principle missing

One should add the maximum principle $H_{u}=0$ to the necessary conditions. Only conditions for $H_{x}$ and $H_{\lambda }$ are listed in the first section. — Preceding unsigned comment added by 194.96.119.238 (talk) 17:15, 27 October 2022 (UTC)

Incomprehensible

What is the L-function? What is the f-function? It is absolutely unclear what this article is about? — Preceding unsigned comment added by 213.219.161.110 (talk) 20:52, 12 June 2011 (UTC)

I reversed the order of Definition and Notation sections, Notation now first, should make it easier to read. Encyclops (talk) 23:56, 12 June 2011 (UTC)

It would be great if the author could put a bit more into the definition. In the comment below Encyclops mentions that the "Hamiltonian is just a mathematical expression which occurs in the Principle" Perhaps starting with a statement like this would help provide the uninitiated with a bit more context?

The Hamiltonian of Optimal Control Theory is a mathematical expression which occurs in Pontryagin's minimum principle. — Preceding unsigned comment added by 148.107.2.20 (talk) 16:27, 27 May 2014 (UTC)

The article still is absolutely unclear. What do the brackets <.,.> mean? What is "the article by Sussmann and Willems" and why should we care that the given definition agrees with it? What is the brachystochrone problem? What are p and q, how do they relate to x and u? — Preceding unsigned comment added by 134.58.253.57 (talk) 16:06, 5 August 2015 (UTC)

Merge Hamiltonian (control theory) and Pontryagin's minimum principle

• Support - Both articles deal with the same topic - Nmnogueira 16:07, 6 June 2007 (UTC)

Which title? Smmurphy^(Talk) 22:23, 6 June 2007 (UTC)

I would keep "Pontryagin's minimum principle" - Nmnogueira 19:24, 7 June 2007 (UTC)

• Oppose - No harm in having both articles. Encyclops 17:25, 9 June 2007 (UTC)

Perhaps true, if we talked about different interpretations of the Hamiltonian and such in this article. Is there more to your idea? Smmurphy^(Talk) 02:51, 11 June 2007 (UTC)

The entry Pontryagin's minimum principle is the more important of the two. The Hamiltonian is just a mathematical expression which occurs in the principle. But I think it is important there should be an entry for the Hamiltonian so that people who hear about it (perhaps without even having heard of Pontryagin) can look it up. If there is no such entry then people will find information in Wikipedia about the Hamiltonian of physics but will miss the fact that there is another thing called a Hamiltonian in optimal control. (So, yes, this entry is about a different interpretation of the word Hamiltonian). A problem with this entry is that it restates the minimum principle and therefore unfortunately duplicates some of the material in Pontryagin's minimum principle. The solution to this is not to kill off this entry but to rewrite it in such a way that it refers to the other entry. Encyclops 00:55, 12 June 2007 (UTC)

severe harm from having two articles on the same topic, editing goes to two articles that makes two okay articles instead of one good one. 129.2.19.149 14:20, 26 June 2007 (UTC)

Check the new version! It should go a long way to meeting your objections. Encyclops 14:21, 30 June 2007 (UTC)

The important question is: what application does the control Hamiltonian have apart from the from the Pontryagin Principle? There is the odd paper which attempts to apply it to classical dynamics but that is not yet an established theory. I must say though that the new article on control Hamiltonian is much more clearly written than the Ponryagin one which which is confusing.JFB80 (talk) 08:35, 30 July 2014 (UTC)

Costate equations

In continuous time, the costate equations show the rate of change of lambda at the left-hand side. This is not so in the discrete time costate equations shown here. Is this correct? If so, does it requires an explanation?

Arie ten Cate (talk) 14:04, 16 September 2011 (UTC)

You are right, there is something unclear in the article (I only now noticed!). It depends how the discrete time problem is defined. If the system state equations are defined as $x=f(x,u,t)$ (This is the simplest form and was the definition in the book I was using) then the Hamiltonian is as given. But sometimes the system is defined as $x(t)-x(t-1)=f(x,u,t)$ which is closer to the continuous time form, in that case the Hamiltonian is different. The definition of the problem needs to be given, and a reference to the book (in case of future doubts) needs to be added. Encyclops (talk) 01:26, 18 September 2011 (UTC)

I think the discrete time formulation needs to be rewritten to be for dynamics in the $x_{t+1}=f(x_{t},u_{t},t)$ form. At least from my experience the $x_{t+1}-x_{t}=f(x_{t},u_{t},t)$ form is not common unless you are doing simple Euler discretization. Besides, the $x_{t+1}=f(x_{t},u_{t},t)$ form is more general. This should make the costate equations be of the form $\lambda _{t}={\frac {\partial H}{\partial x_{t}}}$. 35.1.2.215 (talk) 23:17, 19 January 2023 (UTC)

Add class macroeconomic example of maximizing lifetime utility given wealth process

I believe it would be beneficial to add an example of maximizing lifetime utility subject to an income/savings flow. I am new to editing in wikipedia but I am up for the task! As an economics PhD student, I'd like to spread the knowledge! Alexnally (talk) 21:33, 21 July 2018 (UTC)

Link [10] is broken

The link [10] to "Over 300 years of control theory" is broken. — Preceding unsigned comment added by Ronald L. Rivest (talk • contribs) 04:08, 10 March 2020 (UTC)