# Questions tagged [optimal-control]

Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. (Def: http://en.m.wikipedia.org/wiki/Optimal_control)

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### How to solve second order differential optimal control or optimization problem？

From a long time, I meet an optimal control problem, but i don't know how to solve it. Well, to be more specific, Suppose we have following dynamic system and cost function, \begin{cases} \ddot{y}=\...
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### proof of the existence of a bang bang control

I was reading the proof of the existence of the bang bang control throughout the theory of the L infinty space; however i got stuck at a piece of the proof. I am sure im overcomplicating the problem ...
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### Any stabilizing control law $K$ is optimal for some LQR problems ($Q$ and $R$).

I recently went through Kalman's paper "When is a Linear Control System Optimal" published in 1964. The paper makes me wonder whether the following statement is true: Any stabilizing control ...
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### Derivatives of a 2D B-spline with respect to the control points

I'm dealing with an optimal control problem and I want to solve it with the B-splines. In order to compute the gradient of my objective function, I have to derive the B-spline with respect to the ...
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### Showing that $x^*(t)=\sin(t)$ minimizes the functional $J(x(t)) = \int_0^{\pi/2} [\dot x(t)^2 - x(t)^2 ]dt$

We are given the functional $$J(x(t)) = \int_0^{\pi/2} [\dot x(t)^2 - x(t)^2 ]dt$$ with the fixed boundary condition $x(0)=0$ and $x(\frac{\pi}{2})=1$. Could anyone help me prove that $x^*(t)=\sin(t)$ ...
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### Why do optimal control and reinforcement learning use different notation?

In optimal control, state is $x$, control is $u$, and dynamics are $\dot{x}=f(x,u)$. In reinforcement learning, state is $s$, action is $a$, and dynamics are $s'\sim P(s'|s,a)$. I'm curious why these ...
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### Determining the number of switching times in a bang-bang control with nonlinear switching function

In optimal control, if the Hamiltonian $H$ is linear in the control $u$, then the optimality condition $$\frac{\partial H}{\partial u}$$ gives no information about the optimal control $u^*$. The way ...