Questions tagged [optimal-control]
The optimal-control tag has no usage guidance.
14
questions
1
vote
1
answer
64
views
Inconsistent solutions to linear optimal control problem
Consider the following optimal control problem:
\begin{align}
J(t) = \inf_{u(t)} \ & \frac{1}{2} \int_0^\infty e^{-\delta t} \left( x(t)^2 + \lambda y(t)^2 \right) dt \\
s.t. \ &u(t) \geq - \...
- 123
1
vote
0
answers
35
views
Optimal control problem with bounded control
Let's consider the following deterministic constrained optimisation problem, where $c(t)$ is the control, and $x(t)$ and $y(t)$ are the state variables:
\begin{align}
J(t) = \inf_{c(t)} \ &\int_0^\...
- 123
0
votes
0
answers
84
views
Resource allocation problem - RL or stochastic optimization?
I am currently working on a resource allocation problem and I am uncertain about which field of stochastic optimization and reinforcement learning encompasses this particular problem.
The objective is ...
3
votes
0
answers
50
views
Control variables and cofounding effects in stochastic programming/,model predictive control/reinforcement learning
How can we be sure that confounding variables/control variables don’t pickup the effect our decisions w.r.t decision variables had on the actual control variable?
Since the term control variable ...
3
votes
0
answers
32
views
How to establish the optimal value functions and optimal control policy for a controlled random walk problem?
Question: How to establish an explicit characterization of both the optimal value functions and the optimal control policy for a controlled random walk?
Background:
Assume our system is a perfectly-...
- 141
6
votes
1
answer
90
views
Minimize $\int_0^\infty g'(x)f(x)\,dx$ where $f(x)$ has a log-normal density
I would like to optimize (minimize) the following expression in order to find the functional minimizer $g$ (which should be at least once differentiable): $$ \int_0^\infty g'(x) f(x) \ dx $$ where $f(...
- 63
7
votes
5
answers
2k
views
Fast way to repeatedly solve many similar LPs/QPs in parallel
I am running a simulation where I need to repeatedly solve a set of LPs or QPs with slightly different input parameters for a Model Predictive Control application. The problem is I need it to be fast, ...
- 131
1
vote
0
answers
144
views
Simple inventory control with stochastic demand
There is a factory that produces one unit of stock uniformly so that $q$ units of stock are produced during a day. The warehouse near a factory has the maximal capacity of $q$ items, i.e. a daily ...
- 11
5
votes
0
answers
54
views
What kind of algorithm is this: water foraging
I am pondering if a machine learning problem might be better formulated as a reinforcement or control problem. I have no experience with the latter, so bear with me.
Let's say I am organising a tour ...
- 249
3
votes
1
answer
124
views
How to evaluate the convexity of an optimal control problem?
Can we consider an optimal control problem, a convex optimization problem like static optimization problems? If it is possible, under what conditions, will this problem be a convex problem? For ...
- 2,160
4
votes
1
answer
80
views
Optimize probability parameter in an optimal control problem
We have a game with infinite but countable rounds. We have one machine, that may either break down, or continue operating. For each round the machine operates, it gives cost $-1$ (so profit of $1$). ...
- 4,010
8
votes
2
answers
209
views
Conditions for minima in calculus of variations
In the calculus of variations (unconstrained), one applies a first-order variation on a general functional of the form
$$\int_{a}^{b}F(x,y,y')\,dx$$
to obtain the first-order necessary condition for ...
- 725
5
votes
0
answers
44
views
In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples
Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion.
...
- 489
9
votes
2
answers
613
views
Integer Decision Variables Always Forced to Zero in Minimization Problem (MINLP)
I am trying to write out a MINLP problem of optimal control for an invasive species and the code that I have for my PYOMO model is below. Some of the initialization values take from an Excel ...
- 2,319