Merge branch 'CosimoRusso-fixes-2020-07-28'

.gitignore

@@ -12,3 +12,4 @@
 *.fls
 *.toc
 *.synctex(busy)
+*.ps

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]

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*}
 

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:

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} \\

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

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}

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.
 \[