From 627af29b4e5e6b87aa3003cf481b4eaf2f548399 Mon Sep 17 00:00:00 2001 From: Michael Klamkin Date: Fri, 22 Aug 2025 16:19:04 -0400 Subject: [PATCH] y -> u --- class01/class01_intro.jl | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/class01/class01_intro.jl b/class01/class01_intro.jl index fee2ab0..2e7e538 100644 --- a/class01/class01_intro.jl +++ b/class01/class01_intro.jl @@ -86,7 +86,7 @@ In this course, we are interested in problems with the following structure: \phantom{\substack{(\mathbf u_1,\mathbf x_1)\\\mathrm{s.t.}}}% \!\!\!\!\!\!\!\!\!\!(\mathbf u_1,\mathbf x_1)\in\mathcal X_1(\mathbf x_0)% }{% - \!\!\!\!c(\mathbf x_1,\mathbf y_1)% + \!\!\!\!c(\mathbf x_1,\mathbf u_1)% } +\mathbb{E}_1\Bigl[ \quad \cdots @@ -123,7 +123,7 @@ constraints can be generally posed as: &\mathcal{X}_t(\mathbf{x}_{t-1}, w_t)= \begin{cases} f(\mathbf{x}_{t-1}, w_t, \mathbf{u}_t) = \mathbf{x}_t \\ - h(\mathbf{x}_t, \mathbf{y}_t) \geq 0 + h(\mathbf{x}_t, \mathbf{u}_t) \geq 0 \end{cases} \end{align} ``` @@ -135,7 +135,7 @@ where the outgoing state of the system $\mathbf{x}_t$ is a transformation based on the incoming state, the realized uncertainty, and the control variables. In the Markov Decision Process (MDP) framework, we refer to $f$ as the "transition kernel" of the system. State and control variables are restricted further by additional constraints -captured by $h(\mathbf{x}_t, \mathbf{y}_t) \geq 0$. We +captured by $h(\mathbf{x}_t, \mathbf{u}_t) \geq 0$. We consider policies that map the past information into decisions: $\pi_t : (\mathbf{x}_{t-1}, w_t) \rightarrow \mathbf{x}_t$. In period $t$, an optimal policy is given by the solution of the dynamic equations: