From 72dafaccf47a88f57804cd41155ecca8f02eb43d Mon Sep 17 00:00:00 2001 From: Cosimo Russo Date: Tue, 28 Jul 2020 12:29:04 +0200 Subject: [PATCH 1/2] Fix typos --- lectures/2020-04-21.tex | 4 ++-- lectures/2020-04-22.tex | 2 +- lectures/2020-04-23.tex | 2 +- lectures/2020-05-05.tex | 2 +- lectures/2020-05-07.tex | 2 +- lectures/2020-05-11.tex | 2 +- 6 files changed, 7 insertions(+), 7 deletions(-) diff --git a/lectures/2020-04-21.tex b/lectures/2020-04-21.tex index 86543f8..de2a65f 100644 --- a/lectures/2020-04-21.tex +++ b/lectures/2020-04-21.tex @@ -75,8 +75,8 @@ \subsection{Fully Controllable} \end{bmatrix} \qquad G = \begin{bmatrix} - 0 \\ - 1 + 1 \\ + 0 \end{bmatrix} \end{align*} diff --git a/lectures/2020-04-22.tex b/lectures/2020-04-22.tex index d08a2a7..1baa7dd 100644 --- a/lectures/2020-04-22.tex +++ b/lectures/2020-04-22.tex @@ -3,7 +3,7 @@ \paragraph{Step 2} Singular Value Decomposition (SVD) of $\tilde{H}_{qd}$ \[ - \underbrace{\tilde{H}_{qd}}_{n\times n} = \underbrace{\tilde{U}}_{q\times q} \underbrace{\tilde{S}}_{q\times d} \underbrace{\tilde{V}^T}_{d\times d} + \underbrace{\tilde{H}_{qd}}_{q\times d} = \underbrace{\tilde{U}}_{q\times q} \underbrace{\tilde{S}}_{q\times d} \underbrace{\tilde{V}^T}_{d\times d} \] $\tilde{U}$ and $\tilde{V}$ are unitary matrices. A matrix $M$ is unitary if: diff --git a/lectures/2020-04-23.tex b/lectures/2020-04-23.tex index b910ae0..49e0a40 100644 --- a/lectures/2020-04-23.tex +++ b/lectures/2020-04-23.tex @@ -98,7 +98,7 @@ \] \[ R_3 = \begin{bmatrix} - G & F & F^2G + G & FG & F^2G \end{bmatrix} = \begin{bmatrix} 1 & \frac{1}{2} & \frac{1}{4} \\ 0 & 1 & \frac{3}{4} \\ diff --git a/lectures/2020-05-05.tex b/lectures/2020-05-05.tex index 1d9fad4..64e662d 100644 --- a/lectures/2020-05-05.tex +++ b/lectures/2020-05-05.tex @@ -62,7 +62,7 @@ \subsection{Block-scheme representation of K.F.} Fundamental contribution of Kalman was to find the optimal gain $K(t)$. $K(t)$ is not a simple scalar gain but is a (maybe very large) $n\times p$ matrix. -The section of gain matrix $K(t)$ is very critical: +The selection of gain matrix $K(t)$ is very critical: \begin{itemize} \item If $K(t)$ is \emph{too small}: the estimation is not optimal because we are \emph{under exploiting} the information in $y(t)$ \item If $K(t)$ is \emph{too big}: risk of over-exploiting $y(t)$ and we can get noise amplification, even risk of instability diff --git a/lectures/2020-05-07.tex b/lectures/2020-05-07.tex index 575c901..31aec4e 100644 --- a/lectures/2020-05-07.tex +++ b/lectures/2020-05-07.tex @@ -1,6 +1,6 @@ \newlecture{Sergio Savaresi}{07/05/2020} -To answer those questions we need to fundamental theorems (K.F. asymptotic theorems). +To answer those questions we need two fundamental theorems (K.F. asymptotic theorems). They provide \emph{sufficient} conditions only. \paragraph{First asymptotic theorem} diff --git a/lectures/2020-05-11.tex b/lectures/2020-05-11.tex index d324c16..a5df5e0 100644 --- a/lectures/2020-05-11.tex +++ b/lectures/2020-05-11.tex @@ -143,7 +143,7 @@ \subsection{Extension to Non-Linear systems} $K(t)$ in Extended Kalman Filter can be computed as: \[ - K(t) = \left( F(t) P(t) H(t)^T + V_2 \right) \left( H(t) P(t) H(T)^T + V_2 \right)^{-1} + K(t) = \left( F(t) P(t) H(t)^T + V_{12} \right) \left( H(t) P(t) H(T)^T + V_2 \right)^{-1} \] And $P(t)$ can be computed from D.R.E. \[ From 43a1e681babab6e2c8afe39ed729488608a52b59 Mon Sep 17 00:00:00 2001 From: Edoardo Morassutto Date: Tue, 28 Jul 2020 19:59:37 +0200 Subject: [PATCH 2/2] Fix compilation with the most recent textlive --- .gitignore | 1 + easyclass.cls | 9 ++------- 2 files changed, 3 insertions(+), 7 deletions(-) diff --git a/.gitignore b/.gitignore index a817396..e53cc9e 100644 --- a/.gitignore +++ b/.gitignore @@ -12,3 +12,4 @@ *.fls *.toc *.synctex(busy) +*.ps diff --git a/easyclass.cls b/easyclass.cls index 8a94a99..8a0e911 100644 --- a/easyclass.cls +++ b/easyclass.cls @@ -110,20 +110,15 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Typography, change document font -\RequirePackage[tt=false, type1=true]{libertine} -\RequirePackage[varqu]{zi4} -\RequirePackage[libertine]{newtxmath} +% Typography \RequirePackage[T1]{fontenc} -\RequirePackage[protrusion=true,expansion=true]{microtype} - % Disable paragraph indentation, and increase gap \RequirePackage{parskip} %================================= % header and footer -\RequirePackage{scrpage2} +\RequirePackage{scrlayer-scrpage} \pagestyle{scrheadings} \deftripstyle{pagestyle} % [0.5pt]