diff --git a/Slides/Bode/settings.tex b/Slides/Bode/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/Bode/settings.tex +++ b/Slides/Bode/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/Control/settings.tex b/Slides/Control/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/Control/settings.tex +++ b/Slides/Control/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/ControllabilityObservability/settings.tex b/Slides/ControllabilityObservability/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/ControllabilityObservability/settings.tex +++ b/Slides/ControllabilityObservability/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/Discrete/settings.tex b/Slides/Discrete/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/Discrete/settings.tex +++ b/Slides/Discrete/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/HJB_LQR/main.tex b/Slides/HJB_LQR/main.tex index 9ca416c..29826f5 100644 --- a/Slides/HJB_LQR/main.tex +++ b/Slides/HJB_LQR/main.tex @@ -147,7 +147,7 @@ We can find control that delivers minimum to the function \eqref{eq:HJB_0}: \begin{equation} -u^* = \underset{\bo{u}}{\argmin} \ +u^* = \underset{\bo{u}}{\text{argmin}} \ \left[ g(\bo{x}, \bo{u}) + \frac{\partial J^*}{\partial \bo{x}} \bo{f} (\bo{x}, \bo{u}) \right] diff --git a/Slides/HJB_LQR/settings.tex b/Slides/HJB_LQR/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/HJB_LQR/settings.tex +++ b/Slides/HJB_LQR/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/Introduction/settings.tex b/Slides/Introduction/settings.tex index c7843e7..2f12c66 100644 --- a/Slides/Introduction/settings.tex +++ b/Slides/Introduction/settings.tex @@ -33,6 +33,8 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} @@ -50,9 +52,6 @@ \definecolor{mydarkpink}{RGB}{155, 25, 60} \definecolor{mywhitepink}{RGB}{255, 240, 240} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} - \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/Kalman/main.tex b/Slides/Kalman/main.tex index 1ba40de..d3d4781 100644 --- a/Slides/Kalman/main.tex +++ b/Slides/Kalman/main.tex @@ -2,6 +2,12 @@ \input{settings.tex} +\newcommand{\db}[1] {\dot{\mathbf{#1}}} +\newcommand{\bhat}[1] {\hat{\mathbf{#1}}} +\newcommand{\dhat}[1] {\dot{\hat{\mathbf{#1}}}} +\newcommand{\btil}[1] {\Tilde{\mathbf{#1}}} +\newcommand{\dtil}[1] {\dot{\Tilde{\mathbf{#1}}}} + \title{Kalman Filter} \subtitle{Control Theory, Lecture 10} @@ -336,7 +342,7 @@ \end{cases} \end{equation} - where $\bhat{x}_{i+1}^-$ is an \emph{a priori} estimate. \textcolor{mygray2}{We can re-write the last equation as + where $\bhat{x}_{i+1}^-$ is an \emph{a priori} estimate. \textcolor{mylightgray}{We can re-write the last equation as $\bhat{x}_{i+1} = \bhat{x}_{i+1}^- + \bo{L}_i (\bo{H} \bo{x}_i - \bo{H} \bhat{x}_{i+1}^- + \bo{v}_i) $.} \bigskip diff --git a/Slides/Kalman/settings.tex b/Slides/Kalman/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/Kalman/settings.tex +++ b/Slides/Kalman/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/LMI/settings.tex b/Slides/LMI/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/LMI/settings.tex +++ b/Slides/LMI/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/Laplace/settings.tex b/Slides/Laplace/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/Laplace/settings.tex +++ b/Slides/Laplace/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/Linearization/settings.tex b/Slides/Linearization/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/Linearization/settings.tex +++ b/Slides/Linearization/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/LyapunovTheory/settings.tex b/Slides/LyapunovTheory/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/LyapunovTheory/settings.tex +++ b/Slides/LyapunovTheory/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/Observer/settings.tex b/Slides/Observer/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/Observer/settings.tex +++ b/Slides/Observer/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250} diff --git a/Slides/Stability/settings.tex b/Slides/Stability/settings.tex index 7c43e5d..2f12c66 100644 --- a/Slides/Stability/settings.tex +++ b/Slides/Stability/settings.tex @@ -33,17 +33,24 @@ \definecolor{mygreen}{RGB}{0, 200, 0} \definecolor{mygreen2}{RGB}{245, 255, 230} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} + \definecolor{mygray}{gray}{0.8} \definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} \definecolor{mydarkred}{RGB}{160, 30, 30} \definecolor{mylightred}{RGB}{255, 150, 150} \definecolor{myred}{RGB}{200, 110, 110} \definecolor{myblackred}{RGB}{120, 40, 40} -\definecolor{mygreen}{RGB}{0, 200, 0} -\definecolor{mygreen2}{RGB}{205, 255, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} \definecolor{mydarkcolor}{RGB}{60, 25, 155} \definecolor{mylightcolor}{RGB}{130, 180, 250}