# Tag Info

## Hot answers tagged optimal-control

Accepted

### When Optimal Control fails (?)

I believe the problem is that the steady state may not exist, and the system instead exhibits steady growth (depending on parameters). The reason is because the model is equivalent to the standard ...
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### When Optimal Control fails (?)

I am posting this as an answer, because it continues on user @ivansml answer... which is the one that identified the catch here, a catch I naively have overlooked (although it is a narrow case, while ...
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### Does control system engineering have a place in economics?

Economists have been exploring control theory applications to macro economics for decades. For example, here is a 40 year-old research paper written in 1976 on the topic. top of page 2 (also numbered ...
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### Current Value Hamiltonian VS Present Value Hamiltonian in Economics

There is no clear right and wrong about this, it's just a matter of convenience. The current-value Hamiltonian is likely to be more convenient when the objective function includes a discount factor. ...
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### Euler equation in Continuous time VS Discrete time

One way to see (intuitively) the connection between the left hand sides is to write the discrete case as: $$\frac{u'(c(t + \tau))}{u'(c(t))},$$ for $\tau = 1$. Now if we generalise this to a setting ...
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### Deriving the Euler equation from a Continuous Time Dynamic Programming Problem (HJB)

As already commented, the equation you probably meant is $$\rho V(k)= \sup_c \{\, u(c) + V'(k) ( f(k) -\delta k -c ) \,\}.$$ I have never seen this equation called the HJB equation (probably missing ...
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### When Optimal Control fails (?)

I think that the key question is whether this firm is the only firm in the economy. If it is then it is no longer correct for it to take $w$ as given as $w$ will be affected by its own capital ...

### Autonomous or non-autonomous optimal control system?

Following Caputo, an Optimal Control problem is autonomous when none of the functions appearing in the description of the problem depends explicitly on the time-variable. But this means that the ...
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### Autonomous or non-autonomous optimal control system?

What about rewriting the problem in the following way? $$\underset{\left\{ c_{t}\right\} }{max}\int_{t=0}^{\infty}\left[u\left(c_{t}\right) e^{y_t}\right]e^{-\rho t}dt$$ with the new state variables ...
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### What is state space representation for DSGE modeling

This question is too broad as it stands. There is a longer answer already, but I think it is possible to deal with a core part of the question easily. The concrete question is what is a state-space ...
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### Does control system engineering have a place in economics?

For a PID system to work, you need to be (at least approximately) correct about the relationship between the variables you are trying to manage. Unfortunately the relationships between macroeconomic ...
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### Autonomous or non-autonomous optimal control system?

I think I proved in a rigorous way that the system is autonomous for the model that I have written 3-4 days and I think it is useful for the community, especially for those who are working on ...
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