From 81bc58ba7169dbc852e06440bf4f2a699649a06a Mon Sep 17 00:00:00 2001 From: youainti Date: Tue, 16 Nov 2021 19:34:55 -0800 Subject: [PATCH] Got most of the presentation finished --- .../Presentation/Presentation.tex | 209 ++++++++++++++---- 3rdyearpresentation/outline2.txt | 3 +- CurrentWriting/sections/05_SocialPlanner.tex | 2 +- 3 files changed, 171 insertions(+), 43 deletions(-) diff --git a/3rdyearpresentation/Presentation/Presentation.tex b/3rdyearpresentation/Presentation/Presentation.tex index df0f6d6..6fcbd0d 100644 --- a/3rdyearpresentation/Presentation/Presentation.tex +++ b/3rdyearpresentation/Presentation/Presentation.tex @@ -56,12 +56,6 @@ Washington State University \\ % Your institution for the title page \end{frame} -\begin{frame}[allowframebreaks] %Allow frame breaks -\frametitle{Overview} % Table of contents slide, comment this out to remove it -\tableofcontents -%Planned TOC -% See ../outline2.txt -\end{frame} %------------------------------------------------------------------------------------- %%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%% @@ -75,25 +69,105 @@ Washington State University \\ % Your institution for the title page % % %------------------------------------------------------------------------------------- +\begin{frame} + \frametitle{Orbital Debris} + %Story from monday ISS + + Recent News: + \begin{itemize} + \item Russion conducts an Anti-Satellite Missle Test generating at least 1,500 items of trackable debris + \item The Astronauts and Cosmonauts on the ISS entered lockdown, including donning pressure suits. + \item The situation is still being monitored although the immediate danger appears to have passed. + \end{itemize} + + \url{https://edition.cnn.com/2021/11/15/politics/russia-anti-satellite-weapon-test-scn/index.html} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Orbital Debris} + Other recent events highlight the dangers from orbital debris: + \begin{itemize} + \item ISS conducts 3 evasive maneuvers to doge debris in 2020- + \href{https://www.jpost.com/science/international-space-station-nearly-struck-by-chinese-satellite-debris-684809}{Jerusalem Post} + \item ISS hit by debris, May 2021- \href{https://www.asc-csa.gc.ca/eng/iss/news.asp}{Canadian Space Agency} + \item ISS dodged debris from 2007 Anti-Sat Missile, Nov 2021- + \href{https://www.jpost.com/science/international-space-station-nearly-struck-by-chinese-satellite-debris-684809}{Jerusalem Post (Same as above)} + \end{itemize} + + %This isn't a unique experience + %list of other issues the ISS has faced + +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Orbital Debris} + %Talk about Fregat breakup + Not just an issue for manned space flight. + \begin{itemize} + \item In May of 2020, the Satellite SL-23 Zenit Fregat's + tank suffered a second breakup event. + \item While only 65 large pieces of debris were initially identified, by Feb. 2021 + over 325 had been attributed to the breakup. + \item Debris was spread in orbits between 500km and 6,000km. + \end{itemize} + + \href{https://www.orbitaldebris.jsc.nasa.gov/quarterly-news/pdfs/odqnv25i1.pdf}{Orbital Debris Quarterly News - NASA} + +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Why now?} + %launch costs + %nano-satellites + In recent years two major changes have occured + \begin{enumerate} + \item SpaceX: Plummeting Launch costs + \item CubeSates and other Nano-Satellites. + \end{enumerate} +\end{frame} +%------------------------------- +\begin{frame} + \frametitle{Goal of the Paper} + %Model decision making of satellite operators to be able to investigate policies to reduce kessler syndrome. + + \center + Project Goals: + \begin{itemize} + \item Model the choices + facing Satellite Constellation Operators + and optimal policy policy response. + \item Investigate the effect of various policies on debris pollution + \end{itemize} +\end{frame} +%------------------------------- +%------------------------------------------------------------------------------------- +%%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%% +\section{TOC} +%------------------------------------------------------------------------------------- +\begin{frame}[allowframebreaks] %Allow frame breaks +\frametitle{Overview} % Table of contents slide, comment this out to remove it +\tableofcontents +%Planned TOC +% See ../outline2.txt +\end{frame} %------------------------------------------------------------------------------------- %%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%% \section{Literature} %------------------------------------------------------------------------------------- \begin{frame} \frametitle{Past Literature} + + Key elements of recent literature. \begin{enumerate} - \item Kessler and Cour-Palais: Raised issue of orbital pollution - \item Adilov et al: Described 2 period salop model of interactions - \item Adilov et al: Described an infinite period model with symmetric competitive interactions. - \item Rao and Rondina: Describe a symetric infinite period model (first to do so). + \item \cite{Kessler1978}: Raised issue of runaway orbital pollution. + \item \cite{Adilov2015}: Described 2 period salop model of interactions. + \item \cite{Adilov2018,Adilov2018a}: Described an infinite period model with symmetric competitive interactions. + \item \cite{RaoRondina2020}: Describe a symetric infinite period model (first to do so). + \item \cite{Rao2020}: Examine the effect of Orbital-Use fees, find it would quadruple long term value produced of the space industry. \end{enumerate} \end{frame} %------------------------------- -\begin{frame} - \frametitle{} -\end{frame} -%------------------------------- %------------------------------------------------------------------------------------- %%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%% \section{Model} @@ -113,9 +187,11 @@ Washington State University \\ % Your institution for the title page \begin{frame} \frametitle{Mathematical Notation} \begin{itemize} - \item $\{s^j_t\}$: The set of constellation satellites stocks - \item $D_t$: The level of debris - \item $x^j_t$: The launches from each constellation + \item $S_t$: The set of constellation satellites stocks. + \item $s^i_t$: The number of satellites (stock) for constellation $i$. + \item $D_t$: The level of debris. + \item $X_t$: The set of launches. + \item $x^i_t$: The launches from constellation $i$. \item \end{itemize} \end{frame} @@ -129,13 +205,25 @@ Washington State University \\ % Your institution for the title page \begin{align} D_{t+1} =& (1-\delta)D_t \tag{Debris decay.} \\ &+ g\cdot D_t \tag{Debris produced by collision with debris.} \\ - &+ \gamma \sum^N_{i=1} \left(1-R^i(\{s^j_t\},D_t) \right) s^i_t \tag{Debris produced by satellite destruction.} \\ - &+ \Gamma \sum^n_{j=1} \{x^j_t\} \tag{Debris produced by launches.} + &+ \gamma \sum^N_{i=1} \left(1-R^i(S_t,D_t) \right) s^i_t \tag{Debris produced by satellite destruction.} \\ + &+ \Gamma \sum^n_{j=1} x^j_t \tag{Debris produced by launches.} \end{align} \end{frame} %------------------------------- \begin{frame} \frametitle{Satellite Stocks} + + Law of motion for satellite stocks + \begin{align} + s^i_{t+1} =& \left( + R^i(S_t,D_t,X_t) + - \eta + \right) \cdot s^i_t + + x^i_t + \end{align} + \begin{itemize} + \item $\eta$ is the orbit decay rate of satellites. + \end{itemize} \end{frame} %------------------------------- %------------------------------------ @@ -153,7 +241,6 @@ Washington State University \\ % Your institution for the title page \end{block} Often described as a condition with an exponential growth of debris. - Similar to what is expected with Climate Change \end{frame} %------------------------------- \begin{frame} @@ -163,14 +250,14 @@ Washington State University \\ % Your institution for the title page Develops an analog of kessler syndrome where the condition is met when satellites are destroyed immediately after launch by debris. \begin{align} - \left\{ (\{s^j_t\},D_t) : R^i(\{s^j_t\},D_t) = 0 \forall i\right\} + \left\{ (S_t,D_t) : R^i(S_t,D_t) = 0 \forall i\right\} \end{align} \item \cite{RaoRondina2020}:\\ A working paper in which the authors develop a dynamic model and a definition of kessler syndrome that captures all increasing debris levels. \begin{align} - \left\{ (\{s^j_t\},D_t) : - \lim_{t\rightarrow \infty} D_{t+1}(\{s^j_t\},D_t) = \infty + \left\{ (S_t,D_t) : + \lim_{t \rightarrow \infty} D_{t+1}(S_t,D_t) = \infty \right\} \end{align} \end{itemize} @@ -190,7 +277,7 @@ Washington State University \\ % Your institution for the title page \frametitle{$\epsilon$-Kessler Region} \begin{block}{$\epsilon$-Kessler Region} \begin{align} - \kappa = \left\{ \left(\{s^j_t\}, D_t \right) : \forall k \geq 0, + \kappa_\epsilon = \left\{ \left(S_t, D_t \right) : \forall k \geq 0, ~~ D_{t+k+1} - D_{t+k} \geq \epsilon > 0 \right\} \end{align} \end{block} @@ -209,8 +296,9 @@ Washington State University \\ % Your institution for the title page \begin{block}{Proto Kessler Region} \begin{align} + \kappa_\text{proto} = \left\{ - \left(\{s^j_t\},D_t \right) : ~~ D_{t+1} - D_{t} \geq \epsilon_\text{proto} + \left(S_t,D_t \right) : ~~ D_{t+1} - D_{t} \geq \epsilon_\text{proto} \right\} \end{align} \end{block} @@ -242,12 +330,16 @@ Washington State University \\ % Your institution for the title page %------------------------------------ \begin{frame} \frametitle{Operator's Problem} + \begin{align} + V^i(S_t, x^{\sim i}_t, D_t) = \max_{x^i_t} u^i(S_t, D_t) -F(x^i_t) + + \beta \left[ V^i(S_{t+1}, x^{\sim i}_{t+1}, D_{t+1}) \right] + \end{align} \end{frame} %------------------------------- \begin{frame} \frametitle{Benefit Functions} - Possible profit functions + Possible benefit functions \begin{itemize} \item Linear (Currently working on this one) \item Cournot Profits @@ -259,11 +351,26 @@ Washington State University \\ % Your institution for the title page %------------------------------- \begin{frame} \frametitle{Planner's Problem} + \begin{align} + W(S_t, D_t) =& \max_{X_t} \left[ + \sum^N_{i=1} \left(u^i(S_t, D_t) - F(x^i_t) \right) + + \beta \left[ W(S_{t+1}, D_{t+1}) \right]\right] \notag \\ + &\text{subject to:} \notag \\ + & s^i_{t+1} = (R^i(S_t, D_t)) s^i_t +x^i_t ~~~ \forall i \notag \\ + & D_{t+1} = (1-\delta + g)D_t + + \gamma \sum^N_{i=1} \left(1-R^i(\vec s_t, D_t)\right) s^i_t + + \Gamma \sum^N_{i=1} x^i_t + \end{align} \end{frame} %------------------------------- \begin{frame} \frametitle{Planned model expansions} - Multiple interacting orbital shells and debris terms. + \begin{itemize} + \item Multiple interacting orbital shells and debris terms. + \item Stochastic laws of motion + \item Multiple types of operators + \item Operators benefit functions include taxation + \end{itemize} \end{frame} %------------------------------- %------------------------------------------------------------------------------------- @@ -272,11 +379,10 @@ Washington State University \\ % Your institution for the title page %------------------------------------------------------------------------------------- \begin{frame} \frametitle{Issues} - The following issues characterize the Operators' or Planner's problem + The following issues characterize the Operators' and Planner's problem \begin{itemize} \item Curse of Dimensionality - \item Unsure of state space, no idea what equilibrium (if it exists) would look like. - \item Strategic Interaction (Computability issues) + \item Strategic Interaction (operators only) \end{itemize} \end{frame} %------------------------------- @@ -286,9 +392,9 @@ Washington State University \\ % Your institution for the title page Possible approaches \begin{itemize} \item Standard VFI/Howards algorithm. - \item VFI with sparse state space and other computational benefits. - \item Maliar et al's approachs to supervised learning. + \item VFI with sparse state space (dimensionality reduction). \item Reinforcement Learning. + \item \cite{MALIAR2018} approaches using machine learning. \end{itemize} \end{frame} %------------------------------- @@ -298,9 +404,9 @@ Washington State University \\ % Your institution for the title page % present basic approach (using my notation) % Discuss basic training loop (use sutton and bartos term Generalized Policy Iteration) - Bellman Residual minimization \cref{MALIAR2018} + Bellman Residual minimization \autocite{MALIAR2018} - Use NN to approximate $V(S_t,D_t|\theta_1)$ and $X(X_t,D_t|\theta_2)$. + Use NN to approximate $V(S_t,D_t|\theta_1)$ and $X(S_t,D_t|\theta_2)$. The loss function is: \begin{align} @@ -319,24 +425,31 @@ Washington State University \\ % Your institution for the title page \right] \end{align} - Iterate between Value and Policy function estimation. \end{frame} %------------------------------- \begin{frame} \frametitle{Training Loop: Planner} + For each training epoch + \begin{enumerate} + \item Draw random data + \item train policy function + \item train value function + \end{enumerate} \end{frame} %------------------------------- \begin{frame} \frametitle{Training Loop: Operators} - Using a branched policy function and individual value funcitons For each training epoch - Draw random data - For each operator - select operator's policy parameters. - train policy function - train value function + \begin{enumerate} + \item Draw random data + \item For each operator + \begin{enumerate} + \item train policy function + \item train value function + \end{enumerate} + \end{enumerate} \end{frame} %------------------------------- %------------------------------------ @@ -345,6 +458,9 @@ Washington State University \\ % Your institution for the title page \begin{frame} \frametitle{State of the Code} Currently functioning + \begin{itemize} + \item Nothing + \end{itemize} %Planner training %Operator training \end{frame} @@ -353,6 +469,17 @@ Washington State University \\ % Your institution for the title page \frametitle{Results} %simulated debris paths (increase the ammount of debris a couple orders of magnitude) %Protokessler region plots? + + Results are currently waiting on finishing the code. + + \vspace{12pt} + + Some analyses I plan on completing include + \begin{itemize} + \item Trajectory Analysis + \item Free Entry Conditions + \item Kessler Regions + \end{itemize} \end{frame} %------------------------------- %------------------------------------------------------------------------------------- diff --git a/3rdyearpresentation/outline2.txt b/3rdyearpresentation/outline2.txt index c4213e7..6093552 100644 --- a/3rdyearpresentation/outline2.txt +++ b/3rdyearpresentation/outline2.txt @@ -4,7 +4,8 @@ Why do we care Possible stories: sep 2019 - 2020 - 3 near misses with ISS (https://www.jpost.com/science/international-space-station-nearly-struck-by-chinese-satellite-debris-684809) (https://orbitaldebris.jsc.nasa.gov/quarterly-news/pdfs/odqnv24i3.pdf) + 2020 - 3 near misses with ISS (https://www.jpost.com/science/international-space-station-nearly-struck-by-chinese-satellite-debris-684809) + (https://orbitaldebris.jsc.nasa.gov/quarterly-news/pdfs/odqnv24i3.pdf) May 2020 - Fregat tank breakup (left debris from 1000 to 6000 miles in altitude) May 2021 - Canadarm2 got hit (https://www.asc-csa.gc.ca/eng/iss/news.asp, part way down) Nov 2021 - Dodge debris from anti-satellite test in 2007 (China) (Jerusalem post above) diff --git a/CurrentWriting/sections/05_SocialPlanner.tex b/CurrentWriting/sections/05_SocialPlanner.tex index f052f14..b9d36f2 100644 --- a/CurrentWriting/sections/05_SocialPlanner.tex +++ b/CurrentWriting/sections/05_SocialPlanner.tex @@ -5,7 +5,7 @@ The Social (Fleet) Planner's problem can be written in the bellman form as: \begin{align} W(S_t, D_t) =& \max_{X_t} \left[ - \left(\sum^N_{i=1} u^i(S_t, D_t) - F(x^i_t) \right) + \sum^N_{i=1} \left( u^i(S_t, D_t) - F(x^i_t) \right) + \beta \left[ W(S_{t+1}, D_{t+1}) \right]\right] \notag \\ &\text{subject to:} \notag \\ & s^i_{t+1} = (R^i(S_t, D_t)) s^i_t +x^i_t ~~~ \forall i \notag \\