我一直使用 overprint 环境来一次显示数学环境的一个元素。问题是，我必须为每张幻灯片重复数学运算。有没有更优雅的方式来做到这一点？这是我的示例代码：
\documentclass[dvipsnames,table,aspectratio=169]{beamer} % 16:9 aspect ratio
%\usetheme{Monterey}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{multirow,multicol} % Allows multirows in equations and multicolumns in slides
\usepackage{setspace} % Allows double spacing with the \doublespacing command
% Change text color
\newcommand{\black}[1]{\textcolor{black}{#1}}
\newcommand{\red}[1]{\textcolor{red}{#1}}
\newcommand{\lightgray}[1]{\textcolor{lightgray}{#1}}
% Bold math variables
\newcommand{\fb}{\mathbf{f}}
\newcommand{\xb}{\mathbf{x}}
\newcommand{\hb}{\mathbf{h}}
\newcommand{\ub}{\mathbf{u}}
\newcommand{\eb}{\mathbf{e}}
\newcommand{\pb}{\mathbf{p}}
\newcommand{\qb}{\mathbf{q}}
\newcommand{\gb}{\mathbf{g}}
\newcommand{\Xb}{\mathbf{X}}
\newcommand{\Zb}{\mathbf{Z}}
\newcommand{\lambdab}{\boldsymbol{\lambda}}
\newcommand{\nub}{\boldsymbol{\nu}}
\newcommand{\mub}{\boldsymbol{\mu}}
\newcommand{\chib}{\boldsymbol{\chi}}
\begin{frame}{Background}{Standard Optimal Control}
\begin{itemize}
\item Standard optimal control problem \cite{ross2015primer}
\end{itemize}
\setstretch{1.5}
\vspace{-1cm}
\begin{overprint}
\onslide<1>
\begin{gather*}
\xb(t) = (x_1(t),\ldots,x_{N_x}(t)) \in \mathbb{R}^{N_x}, \quad
\ub(t) = (u_1(t),\ldots,u_{N_u}(t)) \in \mathbb{R}^{N_u} \\
(\textsf{P}) \left\lbrace
\begin{array}{l l}
\textsf{Minimize} & J[\xb(\cdot),\ub(\cdot),t_0,t_f] = \\
& E(\xb_0,\xb_f,t_0,t_f) + \displaystyle\int_{t_f}^{t_0}F(\xb(t),\ub(t),t)\,dt\\
\textsf{Subject to} & \dot{\xb}(t) = \fb(\xb(t),\ub(t),t) \\
& \eb^L \leq \eb(\xb_0,\xb_f,t_0,t_f) \leq \eb^U \\
& \hb^L \leq \hb(\xb(t),\ub(t),t) \leq \hb^U
\end{array}
\right.
\end{gather*}
\onslide<2>
\lightgray{\begin{gather*}
\black{\xb(t) = (x_1(t),\ldots,x_{N_x}(t)) \in \mathbb{R}^{N_x}, \quad
\ub(t) = (u_1(t),\ldots,u_{N_u}(t)) \in \mathbb{R}^{N_u}} \\
(\textsf{P}) \left\lbrace
\begin{array}{l l}
\textsf{Minimize} & J[\xb(\cdot),\ub(\cdot),t_0,t_f] = \\
& E(\xb_0,\xb_f,t_0,t_f) + \displaystyle\int_{t_f}^{t_0}F(\xb(t),\ub(t),t)\,dt\\
\textsf{Subject to} & \dot{\xb}(t) = \fb(\xb(t),\ub(t),t) \\
& \eb^L \leq \eb(\xb_0,\xb_f,t_0,t_f) \leq \eb^U \\
& \hb^L \leq \hb(\xb(t),\ub(t),t) \leq \hb^U
\end{array}
\right.
\end{gather*}}
\onslide<3>
\lightgray{\begin{gather*}
\xb(t) = (x_1(t),\ldots,x_{N_x}(t)) \in \mathbb{R}^{N_x}, \quad
\ub(t) = (u_1(t),\ldots,u_{N_u}(t)) \in \mathbb{R}^{N_u} \\
(\textsf{P}) \left\lbrace
\begin{array}{l l}
\black{\textsf{Minimize}} & \black{J[\xb(\cdot),\ub(\cdot),t_0,t_f] = }\\
& \black{E(\xb_0,\xb_f,t_0,t_f) + \displaystyle\int_{t_f}^{t_0}F(\xb(t),\ub(t),t)\,dt}\\
\textsf{Subject to} & \dot{\xb}(t) = \fb(\xb(t),\ub(t),t) \\
& \eb^L \leq \eb(\xb_0,\xb_f,t_0,t_f) \leq \eb^U \\
& \hb^L \leq \hb(\xb(t),\ub(t),t) \leq \hb^U
\end{array}
\right.
\end{gather*}}
\onslide<4>
\lightgray{\begin{gather*}
\xb(t) = (x_1(t),\ldots,x_{N_x}(t)) \in \mathbb{R}^{N_x}, \quad
\ub(t) = (u_1(t),\ldots,u_{N_u}(t)) \in \mathbb{R}^{N_u} \\
(\textsf{P}) \left\lbrace
\begin{array}{l l}
\textsf{Minimize} & J[\xb(\cdot),\ub(\cdot),t_0,t_f] = \\
& E(\xb_0,\xb_f,t_0,t_f) + \displaystyle\int_{t_f}^{t_0}F(\xb(t),\ub(t),t)\,dt\\
\black{\textsf{Subject to}} & \black{\dot{\xb}(t) = \fb(\xb(t),\ub(t),t)} \\
& \eb^L \leq \eb(\xb_0,\xb_f,t_0,t_f) \leq \eb^U \\
& \hb^L \leq \hb(\xb(t),\ub(t),t) \leq \hb^U
\end{array}
\right.
\end{gather*}}
\onslide<5>
\lightgray{\begin{gather*}
\xb(t) = (x_1(t),\ldots,x_{N_x}(t)) \in \mathbb{R}^{N_x}, \quad
\ub(t) = (u_1(t),\ldots,u_{N_u}(t)) \in \mathbb{R}^{N_u} \\
(\textsf{P}) \left\lbrace
\begin{array}{l l}
\textsf{Minimize} & J[\xb(\cdot),\ub(\cdot),t_0,t_f] = \\
& E(\xb_0,\xb_f,t_0,t_f) + \displaystyle\int_{t_f}^{t_0}F(\xb(t),\ub(t),t)\,dt\\
\black{\textsf{Subject to}} & \dot{\xb}(t) = \fb(\xb(t),\ub(t),t) \\
& \black{\eb^L \leq \eb(\xb_0,\xb_f,t_0,t_f) \leq \eb^U} \\
& \hb^L \leq \hb(\xb(t),\ub(t),t) \leq \hb^U
\end{array}
\right.
\end{gather*}}
\onslide<6>
\lightgray{\begin{gather*}
\xb(t) = (x_1(t),\ldots,x_{N_x}(t)) \in \mathbb{R}^{N_x}, \quad
\ub(t) = (u_1(t),\ldots,u_{N_u}(t)) \in \mathbb{R}^{N_u} \\
(\textsf{P}) \left\lbrace
\begin{array}{l l}
\textsf{Minimize} & J[\xb(\cdot),\ub(\cdot),t_0,t_f] = \\
& E(\xb_0,\xb_f,t_0,t_f) + \displaystyle\int_{t_f}^{t_0}F(\xb(t),\ub(t),t)\,dt\\
\black{\textsf{Subject to}} & \dot{\xb}(t) = \fb(\xb(t),\ub(t),t) \\
& \eb^L \leq \eb(\xb_0,\xb_f,t_0,t_f) \leq \eb^U \\
& \black{\hb^L \leq \hb(\xb(t),\ub(t),t) \leq \hb^U}
\end{array}
\right.
\end{gather*}}
\onslide<7>
\begin{gather*}
\xb(t) = (x_1(t),\ldots,x_{N_x}(t)) \in \mathbb{R}^{N_x}, \quad
\ub(t) = (u_1(t),\ldots,u_{N_u}(t)) \in \mathbb{R}^{N_u} \\
(\textsf{P}) \left\lbrace
\begin{array}{l l}
\textsf{Minimize} & J[\xb(\cdot),\ub(\cdot),t_0,t_f] = \\
& E(\xb_0,\xb_f,t_0,t_f) + \displaystyle\int_{t_f}^{t_0}F(\xb(t),\ub(t),t)\,dt\\
\textsf{Subject to} & \dot{\xb}(t) = \fb(\xb(t),\ub(t),t) \\
& \eb^L \leq \eb(\xb_0,\xb_f,t_0,t_f) \leq \eb^U \\
& \hb^L \leq \hb(\xb(t),\ub(t),t) \leq \hb^U
\end{array}
\right.
\end{gather*}
\end{overprint}
\end{frame}
\begin{frame}{Background}{Riemann-Stieltjes Optimal Control (cont.)}
\begin{itemize}
\item Continuous $\pb$-domain Riemann-Stieltjes optimal control problem
\end{itemize}
\setstretch{1.5}
\small
\vspace{-0.5cm}
\begin{overprint}
\onslide<1>
\begin{gather*}
\xb \in \mathbb{X} \subseteq \mathbb{R}^{N_x}, \qquad
\ub \in \mathbb{U} \subseteq \mathbb{R}^{N_u}, \qquad
\pb \in supp(\pb) \\
(\textsf{RS}^\infty) \left\lbrace \begin{array}{l l l}
\textsf{Minimize}
& J_{RS}[\xb(\cdot,\cdot),\ub(\cdot),t] := \\
& \displaystyle \int_{supp(\pb)} J_u[\xb(\cdot,\pb),\ub(\cdot),t]\,d\alpha(\pb) & \\
\textsf{Subject to}
& \dot{\xb}(t,\pb) = \fb(\xb(t,\pb),\ub(t),t) &
\multirow{3}{*}{$\left.\vphantom{\begin{matrix}0\\0\\0\end{matrix}}\right\rbrace\,\forall\,\pb$} \\
& \eb_d(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f) \leq \mathbf{0} \\
& \hb_d(\xb(t,\pb),\ub(t),t) \leq \mathbf{0} \\
& \displaystyle \int_{supp(\pb)} \eb_u(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f)\,d\alpha(\pb) \leq \mathbf{0} & \\
& \displaystyle \int_{supp(\pb)} \hb_u(\xb(t,\pb),\ub(t),t)\,d\alpha(\pb) \leq \mathbf{0} &
\end{array}
\right.
\end{gather*}
\onslide<2>
\lightgray{\begin{gather*}
\black{\xb \in \mathbb{X} \subseteq \mathbb{R}^{N_x}, \qquad
\ub \in \mathbb{U} \subseteq \mathbb{R}^{N_u},} \qquad
\red{\pb \in supp(\pb)} \\
(\textsf{RS}^\infty) \left\lbrace \begin{array}{l l l}
\textsf{Minimize}
& J_{RS}[\xb(\cdot,\cdot),\ub(\cdot),t] := \\
& \displaystyle \int_{supp(\pb)} J_u[\xb(\cdot,\pb),\ub(\cdot),t]\,d\alpha(\pb) & \\
\textsf{Subject to}
& \dot{\xb}(t,\pb) = \fb(\xb(t,\pb),\ub(t),t) &
\multirow{3}{*}{$\left.\vphantom{\begin{matrix}0\\0\\0\end{matrix}}\right\rbrace\,\forall\,\pb$} \\
& \eb_d(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f) \leq \mathbf{0} \\
& \hb_d(\xb(t,\pb),\ub(t),t) \leq \mathbf{0} \\
& \displaystyle \int_{supp(\pb)} \eb_u(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f)\,d\alpha(\pb) \leq \mathbf{0} & \\
& \displaystyle \int_{supp(\pb)} \hb_u(\xb(t,\pb),\ub(t),t)\,d\alpha(\pb) \leq \mathbf{0} &
\end{array}
\right.
\end{gather*}}
\onslide<3>
\lightgray{\begin{gather*}
\xb \in \mathbb{X} \subseteq \mathbb{R}^{N_x}, \qquad
\ub \in \mathbb{U} \subseteq \mathbb{R}^{N_u}, \qquad
\pb \in supp(\pb) \\
(\textsf{RS}^\infty) \left\lbrace \begin{array}{l l l}
\black{\textsf{Minimize}}
& \red{J_{RS}[\xb(\cdot,\cdot),\ub(\cdot),t] :=} \\
& \red{\displaystyle \int_{supp(\pb)} J_u[\xb(\cdot,\pb),\ub(\cdot),t]\,d\alpha(\pb)} & \\
\textsf{Subject to}
& \dot{\xb}(t,\pb) = \fb(\xb(t,\pb),\ub(t),t) &
\multirow{3}{*}{$\left.\vphantom{\begin{matrix}0\\0\\0\end{matrix}}\right\rbrace\,\forall\,\pb$} \\
& \eb_d(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f) \leq \mathbf{0} \\
& \hb_d(\xb(t,\pb),\ub(t),t) \leq \mathbf{0} \\
& \displaystyle \int_{supp(\pb)} \eb_u(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f)\,d\alpha(\pb) \leq \mathbf{0} & \\
& \displaystyle \int_{supp(\pb)} \hb_u(\xb(t,\pb),\ub(t),t)\,d\alpha(\pb) \leq \mathbf{0} &
\end{array}
\right.
\end{gather*}}
\onslide<4>
\lightgray{\begin{gather*}
\xb \in \mathbb{X} \subseteq \mathbb{R}^{N_x}, \qquad
\ub \in \mathbb{U} \subseteq \mathbb{R}^{N_u}, \qquad
\pb \in supp(\pb) \\
(\textsf{RS}^\infty) \left\lbrace \begin{array}{l l l}
\textsf{Minimize}
& J_{RS}[\xb(\cdot,\cdot),\ub(\cdot),t] := \\
& \displaystyle \int_{supp(\pb)} J_u[\xb(\cdot,\pb),\ub(\cdot),t]\,d\alpha(\pb) & \\
\black{\textsf{Subject to}}
& \black{\dot{\xb}(t,\red{\pb}) = \fb(\xb(t,\red{\pb}),\ub(t),t)} &
\red{\multirow{3}{*}{$\left.\vphantom{\begin{matrix}0\\0\\0\end{matrix}}\right\rbrace\,\forall\,\pb$}} \\
& \eb_d(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f) \leq \mathbf{0} \\
& \hb_d(\xb(t,\pb),\ub(t),t) \leq \mathbf{0} \\
& \displaystyle \int_{supp(\pb)} \eb_u(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f)\,d\alpha(\pb) \leq \mathbf{0} & \\
& \displaystyle \int_{supp(\pb)} \hb_u(\xb(t,\pb),\ub(t),t)\,d\alpha(\pb) \leq \mathbf{0} &
\end{array}
\right.
\end{gather*}}
\onslide<5>
\lightgray{\begin{gather*}
\xb \in \mathbb{X} \subseteq \mathbb{R}^{N_x}, \qquad
\ub \in \mathbb{U} \subseteq \mathbb{R}^{N_u}, \qquad
\pb \in supp(\pb) \\
(\textsf{RS}^\infty) \left\lbrace \begin{array}{l l l}
\textsf{Minimize}
& J_{RS}[\xb(\cdot,\cdot),\ub(\cdot),t] := \\
& \displaystyle \int_{supp(\pb)} J_u[\xb(\cdot,\pb),\ub(\cdot),t]\,d\alpha(\pb) & \\
\black{\textsf{Subject to}}
& \dot{\xb}(t,\pb) = \fb(\xb(t,\pb),\ub(t),t) &
\red{\multirow{3}{*}{$\left.\vphantom{\begin{matrix}0\\0\\0\end{matrix}}\right\rbrace\,\forall\,\pb$}} \\
& \black{\eb_d(\xb(t_0,\red{\pb}),\xb(t_f,\red{\pb}),t_0,t_f) \leq \mathbf{0}} \\
& \black{\hb_d(\xb(t,\red{\pb}),\ub(t),t) \leq \mathbf{0}} \\
& \displaystyle \int_{supp(\pb)} \eb_u(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f)\,d\alpha(\pb) \leq \mathbf{0} & \\
& \displaystyle \int_{supp(\pb)} \hb_u(\xb(t,\pb),\ub(t),t)\,d\alpha(\pb) \leq \mathbf{0} &
\end{array}
\right.
\end{gather*}}
\onslide<6>
\lightgray{\begin{gather*}
\xb \in \mathbb{X} \subseteq \mathbb{R}^{N_x}, \qquad
\ub \in \mathbb{U} \subseteq \mathbb{R}^{N_u}, \qquad
\pb \in supp(\pb) \\
(\textsf{RS}^\infty) \left\lbrace \begin{array}{l l l}
\textsf{Minimize}
& J_{RS}[\xb(\cdot,\cdot),\ub(\cdot),t] := \\
& \displaystyle \int_{supp(\pb)} J_u[\xb(\cdot,\pb),\ub(\cdot),t]\,d\alpha(\pb) & \\
\black{\textsf{Subject to}}
& \dot{\xb}(t,\pb) = \fb(\xb(t,\pb),\ub(t),t) &
\multirow{3}{*}{$\left.\vphantom{\begin{matrix}0\\0\\0\end{matrix}}\right\rbrace\,\forall\,\pb.$} \\
& \eb_d(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f) \leq \mathbf{0} \\
& \hb_d(\xb(t,\pb),\ub(t),t) \leq \mathbf{0} \\
& \red{\displaystyle \int_{supp(\pb)} \eb_u(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f)\,d\alpha(\pb) \leq \mathbf{0}} & \\
& \red{\displaystyle \int_{supp(\pb)} \hb_u(\xb(t,\pb),\ub(t),t)\,d\alpha(\pb) \leq \mathbf{0}} &
\end{array}
\right.
\end{gather*}}
\onslide<7->
\begin{gather*}
\xb \in \mathbb{X} \subseteq \mathbb{R}^{N_x}, \qquad
\ub \in \mathbb{U} \subseteq \mathbb{R}^{N_u}, \qquad
\pb \in supp(\pb) \\
(\textsf{RS}^\infty) \left\lbrace \begin{array}{l l l}
\textsf{Minimize}
& J_{RS}[\xb(\cdot,\cdot),\ub(\cdot),t] := \\
& \displaystyle \int_{supp(\pb)} J_u[\xb(\cdot,\pb),\ub(\cdot),t]\,d\alpha(\pb) & \\
\textsf{Subject to}
& \dot{\xb}(t,\pb) = \fb(\xb(t,\pb),\ub(t),t) &
\multirow{3}{*}{$\left.\vphantom{\begin{matrix}0\\0\\0\end{matrix}}\right\rbrace\,\forall\,\pb.$} \\
& \eb_d(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f) \leq \mathbf{0} \\
& \hb_d(\xb(t,\pb),\ub(t),t) \leq \mathbf{0} \\
& \displaystyle \int_{supp(\pb)} \eb_u(\xb(t_0,\pb),\xb(t_f,\pb),t_0,t_f)\,d\alpha(\pb) \leq \mathbf{0} & \\
& \displaystyle \int_{supp(\pb)} \hb_u(\xb(t,\pb),\ub(t),t)\,d\alpha(\pb) \leq \mathbf{0} &
\end{array}
\right.
\end{gather*}
\end{overprint}
\end{frame}
答案1
\textcolor或等命令\color可以感知叠加层。这意味着您无需多次重复内容，而是可以指定\color<2->{lightgray} ...颜色应在哪些叠加层上改变：
\documentclass[dvipsnames,table,aspectratio=169]{beamer} % 16:9 aspect ratio
%\usetheme{Monterey}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{multirow} % Allows multirows in equations
\usepackage{setspace} % Allows double spacing with the \doublespacing command
% Change text color
\newcommand{\black}[1]{\textcolor{black}{#1}}
\newcommand{\red}[1]{\textcolor{red}{#1}}
\newcommand{\lightgray}[1]{\textcolor{lightgray}{#1}}
% Bold math variables
\newcommand{\fb}{\mathbf{f}}
\newcommand{\xb}{\mathbf{x}}
\newcommand{\hb}{\mathbf{h}}
\newcommand{\ub}{\mathbf{u}}
\newcommand{\eb}{\mathbf{e}}
\newcommand{\pb}{\mathbf{p}}
\newcommand{\qb}{\mathbf{q}}
\newcommand{\gb}{\mathbf{g}}
\newcommand{\Xb}{\mathbf{X}}
\newcommand{\Zb}{\mathbf{Z}}
\newcommand{\lambdab}{\boldsymbol{\lambda}}
\newcommand{\nub}{\boldsymbol{\nu}}
\newcommand{\mub}{\boldsymbol{\mu}}
\newcommand{\chib}{\boldsymbol{\chi}}
\begin{document}
\begin{frame}{Background}{Standard Optimal Control}
\begin{itemize}
\item Standard optimal control problem \cite{ross2015primer}
\end{itemize}
\setstretch{1.5}
\vspace{-1cm}
\begin{overprint}
\color<2->{lightgray}\begin{gather*}
\black{\xb(t) = (x_1(t),\ldots,x_{N_x}(t)) \in \mathbb{R}^{N_x}, \quad
\ub(t) = (u_1(t),\ldots,u_{N_u}(t)) \in \mathbb{R}^{N_u}} \\
(\textsf{P}) \left\lbrace
\begin{array}{l l}
\textsf{Minimize} & J[\xb(\cdot),\ub(\cdot),t_0,t_f] = \\
& E(\xb_0,\xb_f,t_0,t_f) + \displaystyle\int_{t_f}^{t_0}F(\xb(t),\ub(t),t)\,dt\\
\textsf{Subject to} & \dot{\xb}(t) = \fb(\xb(t),\ub(t),t) \\
& \eb^L \leq \eb(\xb_0,\xb_f,t_0,t_f) \leq \eb^U \\
& \hb^L \leq \hb(\xb(t),\ub(t),t) \leq \hb^U
\end{array}
\right.
\end{gather*}\color{black}
\end{overprint}
\end{frame}
\end{document}
