Questions tagged [optimal-control]

Question 1

Given distance $S$, time $T>0$ and bounds on the velocity $v_{\min}<v_{\max}$, $$ \begin{array}{ll} \underset{v:[0,T] \to {\Bbb R}}{\text{minimize}} & \displaystyle \int_0^T f(v(t),e(s(t),t))...

Question 2

Given distance $S$, time $T > 0$ and bounds on the velocity $v_{\min} < v_{\max}$, $$ \begin{array}{ll} \underset{v : [0, T] \to {\Bbb R}}{\text{minimize}} & \displaystyle\int_0^T f (v(t),t) ...

Question 3

Let us consider a Lagrangian system for which the equations of motion come from Hamilton's principle and are such that the control variable $\tau$ equals the equations of motion of a free system, ...

Question 4

Given an optimal control problem $$ \begin{cases} \min_{u} &\int_s^T \ell(x(t), u(t)) \, dt + g(x(T))\\ \text{s.t.} & \dot{x}(t) = f(x(t),u(t))\\ & x(s) = x_0\\ & u \in \mathcal{A}\...

Question 5

I am studying a variant of the gambler’s ruin problem and would like help formulating and solving it optimally. A student starts with an initial capital of 3 points. To pass the exam, he must reach 8 ...

Question 6

I am trying to approach this homework on optimal stopping. Suppose we have an optimal stopping problem where we observe the process $$dm_t = \frac{1}{1+t}dW_t,$$ where $W_t$ is a standard Brownian ...

Question 7

Background I'm trying to solve an optimal control problem using Pontryagin's Principle. The problem involves finding a control function that minimizes the time from a given initial state to a given ...

Question 8

For context, I am a layman, although I do have some background in basic college differential equations and linear algebra. I read that one of the drawbacks of control methods based on reinforcement ...

Question 9

Let's say I have an optimal control problem of the following for: \begin{align*} &\max_{\vec{u}}\int_a^bf(\vec{x}(t),\vec{u}(t))\,dt\\[10pt] \text{subject to:}&\qquad \frac{d\vec{x}}{dt}(t) = \...

Question 10

I have read in a number of places that the shortest path between two points $a,b\in \mathbb{R}^2$ that avoids a disk $D$ between them (by "between" I mean the disk intersects the line $a-b$) ...

Question 11

Technically, I am working on an optimal control problem. However, through some trickery, I managed to eliminate the dynamics. What I am left with is the following minimization problem: $$ \min_{g \in ...

Question 12

I have a problem with the proof of Exercise 4.17 iv) in the following script: https://www.maths.ed.ac.uk/~dsiska/LecNotesSCDAA.pdf Here I state the Exercise as in this script together with the ...

Question 13

Let $s\in \left(0, 1\right)$, and consider the task of finding the 'nicest-possible' function $f$ such that $f(0) = 0, f^\prime (0) = s$, and $f(1) = 1, f^\prime (1) = 0$, where 'niceness' is framed ...

Question 14

I have the following misunderstanding regarding observability and observer. Observability of a linear dynamical system is the same as the "recoverability" of the initial condition $x(0)$. A ...

Question 15

I have made great efforts on the derivation, and the results are really close but I am still missing the last step. If someone can help that'd be great! Problem setup Consider this modified Kalman ...

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Questions tagged [optimal-control]

How to solve this kind of constraint optimization problem? [closed]

Solution to a constrained optimal control problem — is $v(t) = \frac{S}{T}$ optimal? [closed]

Are the motion equations of an optimal control problem geodesics on a manifold?

Adjoint state coming from Pontryagin Maximum Principle is normal to the attainable set - Reference Search

Optimal betting strategy to reach 8 points before 0 with success probability 0.4

Continuity of an optimal stopping value with discontinuous gain function.

How to apply Pontryagin's principle to a certain minimum-time problem

Why Is it Difficult to Ensure Stability for RL-based Control Algorithms?

Optimal Control w/ Control Equality Constraints

Proof of shortest path avoiding ball

Minimization with implicit dependency over function spaces

Stochastic Optimal Control: Example of problem with no optimal control

Finding an optimal interpolation subject to some boundary constraints

Why does a Luenberger observer require observability?

Kalman Filter with correlated measurement noise derivation

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