如何用颜色填充两条曲线之间的空间

Question

在一些查询中，我看到有人问如何绘制线性不等式（即如何根据不等式用颜色填充区域）。抱歉，我的代码太长了：

\documentclass[12pt]{article}
\usepackage{pgfplots}
%\pgfplotsset{compat=1.16}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows}
\usepackage{changepage}
\usepackage[margin=1in]{geometry} 
\usepackage{float}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{decorations.markings}
\tikzset{arrow marks/.style={postaction=decorate,decoration={markings,
            mark=between positions #1 and 1 step #1 with {\arrow{>}}}},
    arrow marks/.default=10pt}
\begin{document}
    \begin{figure}[H]
        \begin{adjustwidth}{-0.7in}{-0.7in}
            \centering
            \begin{tikzpicture}
                \def\a{0.5}
                \def\lambda{5}
                \def\xTwoInitPosToZeroOne{1.5}
                \def\xOneInitPosToZeroOne{ln(1 +(\lambda*\a* \xTwoInitPosToZeroOne)/(\lambda + 2*\a*\xTwoInitPosToZeroOne))/(\a^2) - \xTwoInitPosToZeroOne/\a}
                \def\zeroControlPosToNegOne{ln((2*\a* \xTwoInitPosToZeroOne + \lambda)/\lambda)/\a}
                \def\xTwoInitPosToZeroTwo{2}
                \def\xOneInitPosToZeroTwo{ln(1 +(\lambda*\a* \xTwoInitPosToZeroTwo)/(\lambda + 2*\a*\xTwoInitPosToZeroTwo))/(\a^2) - \xTwoInitPosToZeroTwo/\a}
                \def\zeroControlPosToNegTwo{ln((2*\a* \xTwoInitPosToZeroTwo + \lambda)/\lambda)/\a}
                \def\xTwoInitPosToZeroThree{3}
                \def\xOneInitPosToZeroThree{ln(1 +(\lambda*\a* \xTwoInitPosToZeroThree)/(\lambda + 2*\a*\xTwoInitPosToZeroThree))/(\a^2) - \xTwoInitPosToZeroThree/\a}
                \def\zeroControlPosToNegThree{ln((2*\a* \xTwoInitPosToZeroThree + \lambda)/\lambda)/\a}

                \def\xTwoInitNegToZeroOne{-1.5}
                \def\xOneInitNegToZeroOne{-ln(1 -(\lambda*\a* \xTwoInitNegToZeroOne)/(\lambda - 2*\a*\xTwoInitNegToZeroOne))/(\a^2) - \xTwoInitNegToZeroOne/\a}
                \def\zeroControlNegToPosOne{ln((-2*\a* \xTwoInitNegToZeroOne + \lambda)/\lambda)/\a}

                \def\xTwoInitNegToZeroTwo{-2}
                \def\xOneInitNegToZeroTwo{-ln(1 -(\lambda*\a* \xTwoInitNegToZeroTwo)/(\lambda - 2*\a*\xTwoInitNegToZeroTwo))/(\a^2) - \xTwoInitNegToZeroTwo/\a}
                \def\zeroControlNegToPosTwo{ln((-2*\a* \xTwoInitNegToZeroTwo + \lambda)/\lambda)/\a}

                \def\xTwoInitNegToZeroThree{-3}
                \def\xOneInitNegToZeroThree{-ln(1 -(\lambda*\a* \xTwoInitNegToZeroThree)/(\lambda - 2*\a*\xTwoInitNegToZeroThree))/(\a^2) - \xTwoInitNegToZeroThree/\a}
                \def\zeroControlNegToPosThree{ln((-2*\a* \xTwoInitNegToZeroThree + \lambda)/\lambda)/\a}
                \begin{axis}[
                    %xtick distance = {1},
                    %ytick distance = {1},
                    xmin=-12,xmax=12,
                    ymin=-8,ymax=8,
                    height = 7in,width=1.2\textwidth,
                    axis lines=center,
                    axis line style=->, xlabel = {$x_1$}, ylabel={$x_2$},
                    %axis equal,
                    legend cell align = {left},
                    every axis x label/.style={at={(ticklabel* cs:1.05)}, anchor=west,},
                    every axis y label/.style={at={(ticklabel* cs:1.05)}, anchor=south,}, 
                    title= {Bang-off-bang Control Trajectories},         title style={xshift=0, yshift=2em},
                    domain=-15:15,samples=300,legend pos=outer north east]
                    \addplot[->,>=latex,arrow marks=1cm,color = blue, thick, domain = -8:0,tips=proper]({-ln(1-\a*x)/\a^2 - x/\a}, {x}) node[below left, pos = 0.3, font = \small] {\(u^* = 1\)};
                    \addplot[->,>=latex,arrow marks=1cm,color = red, thick, domain = 8:0,tips=proper]({ln(1+\a*x)/\a^2 - x/\a}, {x}) node[above right, pos = 0.3, font = \small] {\(u^* = -1\)};
                    \addplot[dotted, color = black, thick, domain = 8:0,tips=proper]({ln(1+(\lambda*\a*x)/(\lambda + 2*\a*x))/\a^2 - x/\a}, {x});
                    \addplot[dotted, color = black, thick, domain = -8:0,tips=proper]({-ln(1-(\lambda*\a*x)/(\lambda - 2*\a*x))/\a^2 - x/\a}, {x}) node[above right, pos = 0.3, font = \small] {\(u^* = 0\)};

                    %%Starting from here, I am not sure if this is necessary or not
                    \addplot[->,>=latex,arrow marks=1cm, tips = proper,
                    color=red, dashed,thick,domain=-6:0] 
                    ({x/\a + (\xTwoInitPosToZeroOne/\a - 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitPosToZeroOne}, {1/\a + (\xTwoInitPosToZeroOne - 1/\a)*exp(-\a*x)});
                    \addplot[->,>=latex, color=red, tips = proper, dashed,thick,domain=0:\zeroControlPosToNegOne] ({(\xTwoInitPosToZeroOne/\a)*(1 - exp(-\a*x)) + \xOneInitPosToZeroOne}, {\xTwoInitPosToZeroOne*exp(-\a*x)});%1 Pos

                    \addplot[->,>=latex,arrow marks=1cm, tips = proper,
                    color=red, dashed,thick,domain=-6:0] 
                    ({x/\a + (\xTwoInitPosToZeroTwo/\a - 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitPosToZeroTwo}, {1/\a + (\xTwoInitPosToZeroTwo - 1/\a)*exp(-\a*x)});
                    \addplot[->,>=latex, color=red, tips = proper, dashed,thick,domain=0:\zeroControlPosToNegTwo] ({(\xTwoInitPosToZeroTwo/\a)*(1 - exp(-\a*x)) + \xOneInitPosToZeroTwo}, {\xTwoInitPosToZeroTwo*exp(-\a*x)});%2 Pos

                    \addplot[->,>=latex,arrow marks=1cm, tips = proper,
                    color=red, dashed,thick,domain=-6:0] 
                    ({x/\a + (\xTwoInitPosToZeroThree/\a - 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitPosToZeroThree}, {1/\a + (\xTwoInitPosToZeroThree - 1/\a)*exp(-\a*x)});
                    \addplot[->,>=latex, color=red, arrow marks=1cm, tips = proper, dashed,thick,domain=0:\zeroControlPosToNegThree] ({(\xTwoInitPosToZeroThree/\a)*(1 - exp(-\a*x)) + \xOneInitPosToZeroThree}, {\xTwoInitPosToZeroThree*exp(-\a*x)});%3 Pos

                    \addplot[->,>=latex,arrow marks=1cm, tips = proper,
                    color=blue, dashed,thick,domain=-6:0] 
                    ({-x/\a + (\xTwoInitNegToZeroOne/\a + 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitNegToZeroOne}, {-1/\a + (\xTwoInitNegToZeroOne + 1/\a)*exp(-\a*x)});
                    \addplot[->,>=latex, color=blue, tips = proper, dashed,thick,domain=0:\zeroControlNegToPosOne] ({(\xTwoInitNegToZeroOne/\a)*(1 - exp(-\a*x)) + \xOneInitNegToZeroOne}, {\xTwoInitNegToZeroOne*exp(-\a*x)});%1 Neg
                    \addplot[->,>=latex,arrow marks=1cm, tips = proper,
                    color=blue, dashed,thick,domain=-6:0] 
                    ({-x/\a + (\xTwoInitNegToZeroTwo/\a + 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitNegToZeroTwo}, {-1/\a + (\xTwoInitNegToZeroTwo + 1/\a)*exp(-\a*x)});
                    \addplot[->,>=latex, color=blue, tips = proper, dashed,thick,domain=0:\zeroControlNegToPosTwo] ({(\xTwoInitNegToZeroTwo/\a)*(1 - exp(-\a*x)) + \xOneInitNegToZeroTwo}, {\xTwoInitNegToZeroTwo*exp(-\a*x)});%2 Neg
                    \addplot[->,>=latex,arrow marks=1cm, tips = proper,
                    color=blue, dashed,thick,domain=-6:0] 
                    ({-x/\a + (\xTwoInitNegToZeroThree/\a + 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitNegToZeroThree}, {-1/\a + (\xTwoInitNegToZeroThree + 1/\a)*exp(-\a*x)});
                    \addplot[->,>=latex, color=blue, arrow marks = 1cm, tips = proper, dashed,thick,domain=0:\zeroControlNegToPosThree] ({(\xTwoInitNegToZeroThree/\a)*(1 - exp(-\a*x)) + \xOneInitNegToZeroThree}, {\xTwoInitNegToZeroThree*exp(-\a*x)});%3 Neg
                \end{axis}
            \end{tikzpicture}
        \end{adjustwidth} 
        \caption{Optimal control trajectories for Problem 4 for $a = 0.5$ and $\lambda = 5$. The solid plot is the final switching curve, the dotted plot is the switching curve to ``off" mode, while the dashed plots are the state trajectories that are not originally on the switching curve.}
    \end{figure}
\end{document}

我之所以这样写是Starting from here, I am not sure if this is necessary or not因为我不确定颜色填充是否会填满虚线曲线。这是我的输出（带有“高亮”）：

我想要的是，在 LHS（即黑色虚线曲线顶部的左侧和蓝色实线曲线的左侧），我想将该区域涂成红色（或粉红色，具有一定的不透明度），虚线和实线（红色和蓝色）之间的区域涂成橙色（或任何颜色），RHS（即黑色虚线曲线底部的右侧和红色实线的右侧）涂成蓝色（具有一定的不透明度）。有没有办法做到这一点（不覆盖虚线）？

Answer 1

问题是，当使用时fillbetween，路径必须命名，但如果这些路径包括装饰风格，它将不起作用，在这种情况下markings，我不知道为什么，但它不起作用，因为我放置了没有绘图draw=none和样式标记的副本，以便用这些填充区域生成具有一定不透明度的填充，opacity=0.3还添加一些点以便填充整个图形(data)--++(15cm,0);。

结果：

梅威瑟：

\documentclass[12pt]{article}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows,patterns,backgrounds}
\usepackage{changepage}
\usepackage[margin=1in]{geometry} 
\usepackage{float}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{decorations.markings}
\tikzset{arrow marks/.style={postaction=decorate,decoration={markings,
            mark=between positions #1 and 1 step #1 with {\arrow{>}}}},
    arrow marks/.default=10pt}
\begin{document}
    \begin{figure}[H]
        \begin{adjustwidth}{-0.7in}{-0.7in}
            \centering
            \begin{tikzpicture}
            \def\a{0.5}
            \def\lambda{5}
            \def\xTwoInitPosToZeroOne{1.5}
            \def\xOneInitPosToZeroOne{ln(1 +(\lambda*\a* \xTwoInitPosToZeroOne)/(\lambda + 2*\a*\xTwoInitPosToZeroOne))/(\a^2) - \xTwoInitPosToZeroOne/\a}
            \def\zeroControlPosToNegOne{ln((2*\a* \xTwoInitPosToZeroOne + \lambda)/\lambda)/\a}
            \def\xTwoInitPosToZeroTwo{2}
            \def\xOneInitPosToZeroTwo{ln(1 +(\lambda*\a* \xTwoInitPosToZeroTwo)/(\lambda + 2*\a*\xTwoInitPosToZeroTwo))/(\a^2) - \xTwoInitPosToZeroTwo/\a}
            \def\zeroControlPosToNegTwo{ln((2*\a* \xTwoInitPosToZeroTwo + \lambda)/\lambda)/\a}
            \def\xTwoInitPosToZeroThree{3}
            \def\xOneInitPosToZeroThree{ln(1 +(\lambda*\a* \xTwoInitPosToZeroThree)/(\lambda + 2*\a*\xTwoInitPosToZeroThree))/(\a^2) - \xTwoInitPosToZeroThree/\a}
            \def\zeroControlPosToNegThree{ln((2*\a* \xTwoInitPosToZeroThree + \lambda)/\lambda)/\a}

            \def\xTwoInitNegToZeroOne{-1.5}
            \def\xOneInitNegToZeroOne{-ln(1 -(\lambda*\a* \xTwoInitNegToZeroOne)/(\lambda - 2*\a*\xTwoInitNegToZeroOne))/(\a^2) - \xTwoInitNegToZeroOne/\a}
            \def\zeroControlNegToPosOne{ln((-2*\a* \xTwoInitNegToZeroOne + \lambda)/\lambda)/\a}

            \def\xTwoInitNegToZeroTwo{-2}
            \def\xOneInitNegToZeroTwo{-ln(1 -(\lambda*\a* \xTwoInitNegToZeroTwo)/(\lambda - 2*\a*\xTwoInitNegToZeroTwo))/(\a^2) - \xTwoInitNegToZeroTwo/\a}
            \def\zeroControlNegToPosTwo{ln((-2*\a* \xTwoInitNegToZeroTwo + \lambda)/\lambda)/\a}

            \def\xTwoInitNegToZeroThree{-3}
            \def\xOneInitNegToZeroThree{-ln(1 -(\lambda*\a* \xTwoInitNegToZeroThree)/(\lambda - 2*\a*\xTwoInitNegToZeroThree))/(\a^2) - \xTwoInitNegToZeroThree/\a}
            \def\zeroControlNegToPosThree{ln((-2*\a* \xTwoInitNegToZeroThree + \lambda)/\lambda)/\a}
            \begin{axis}[
            %xtick distance = {1},
            %ytick distance = {1},
            xmin=-12,xmax=12,
            ymin=-8,ymax=8,
            height = 7in,width=1.2\textwidth,
            axis lines=center,
            axis line style=->, xlabel = {$x_1$}, ylabel={$x_2$},
            %axis equal,
            legend cell align = {left},
            every axis x label/.style={at={(ticklabel* cs:1.05)}, anchor=west,},
            every axis y label/.style={at={(ticklabel* cs:1.05)}, anchor=south,}, 
            title= {Bang-off-bang Control Trajectories},         title style={xshift=0, yshift=2em},
            domain=-15:15,samples=300,legend pos=outer north east
            ]

            %IV Cuadrant blue plot as path A.
            \addplot[name path=A,->,draw=none,domain = -8:0]({-ln(1-\a*x)/\a^2 - x/\a}, {x});
            \addplot[->,>=latex,arrow marks=1cm,color = blue, thick, domain = -8:0,tips=proper]({-ln(1-\a*x)/\a^2 - x/\a}, {x}) node[below left, pos = 0.3, font = \small] {\(u^* = 1\)};
            %IV Cuadrant dashed black plot as path B.
            \addplot[name path=B,dotted, color = black, thick, domain = -8:0,tips=proper]({-ln(1-(\lambda*\a*x)/(\lambda - 2*\a*x))/\a^2 - x/\a}, {x}) node[above right, pos = 0.3, font = \small] {\(u^* = 0\)};
            %Fill  between A and B
            \addplot[orange,fill opacity=0.2]fill between[of=A and B];

            %II Cuadrant red plot as path C.
            \addplot[name path=C,draw=none, domain = 8:0]({ln(1+\a*x)/\a^2 - x/\a}, {x});
            \addplot[->,>=latex,arrow marks=1cm,color = red, thick, domain = 8:0,tips=proper]({ln(1+\a*x)/\a^2 - x/\a}, {x}) node[above right, pos = 0.3, font = \small] {\(u^* = -1\)};
            %II Cuadrant dashed black plot as path D.
            \addplot[name path=D,dotted, color = black, thick, domain = 8:0,tips=proper]({ln(1+(\lambda*\a*x)/(\lambda + 2*\a*x))/\a^2 - x/\a}, {x});
            %Fill between path C and D
            \addplot[orange,fill opacity=0.2]fill between[of=C and D];


            %%Starting from here, I am not sure if this is necessary or not
            %1st Red arrow marks dashed path E
            \addplot[name path=E,draw=none,domain=0:-6] 
            ({x/\a + (\xTwoInitPosToZeroOne/\a - 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitPosToZeroOne}, {1/\a + (\xTwoInitPosToZeroOne - 1/\a)*exp(-\a*x)})-- ++(-15cm,0);
            \addplot[->,>=latex,arrow marks=1cm, tips = proper,
            color=red, dashed,thick,domain=-6:0] 
            ({x/\a + (\xTwoInitPosToZeroOne/\a - 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitPosToZeroOne}, {1/\a + (\xTwoInitPosToZeroOne - 1/\a)*exp(-\a*x)});
            %complement
            \addplot[name path=E2,draw=none,domain=0:\zeroControlPosToNegOne] ({(\xTwoInitPosToZeroOne/\a)*(1 - exp(-\a*x)) + \xOneInitPosToZeroOne}, {\xTwoInitPosToZeroOne*exp(-\a*x)});%1 Pos
            \addplot[->,>=latex, color=red, tips = proper, dashed,thick,domain=0:\zeroControlPosToNegOne] ({(\xTwoInitPosToZeroOne/\a)*(1 - exp(-\a*x)) + \xOneInitPosToZeroOne}, {\xTwoInitPosToZeroOne*exp(-\a*x)});%1 Pos

            %2nd Red arrow marks dashed path F
            \addplot[name path=F,draw=none,domain=-6:0] 
            ({x/\a + (\xTwoInitPosToZeroTwo/\a - 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitPosToZeroTwo}, {1/\a + (\xTwoInitPosToZeroTwo - 1/\a)*exp(-\a*x)});
            \addplot[->,>=latex,arrow marks=1cm, tips = proper,
            color=red, dashed,thick,domain=-6:0] 
            ({x/\a + (\xTwoInitPosToZeroTwo/\a - 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitPosToZeroTwo}, {1/\a + (\xTwoInitPosToZeroTwo - 1/\a)*exp(-\a*x)});
            %Complement
            \addplot[name path=F2,draw=none,domain=0:\zeroControlPosToNegTwo] ({(\xTwoInitPosToZeroTwo/\a)*(1 - exp(-\a*x)) + \xOneInitPosToZeroTwo}, {\xTwoInitPosToZeroTwo*exp(-\a*x)});%2 Pos
            \addplot[->,>=latex, color=red, tips = proper, dashed,thick,domain=0:\zeroControlPosToNegTwo] ({(\xTwoInitPosToZeroTwo/\a)*(1 - exp(-\a*x)) + \xOneInitPosToZeroTwo}, {\xTwoInitPosToZeroTwo*exp(-\a*x)});%2 Pos
            %Fill between path E and F 
            \addplot[red,fill opacity=0.2]fill between[of=F and E];
            \addplot[red,fill opacity=0.2]fill between[of=F2 and E2];

            \addplot[->,>=latex,arrow marks=1cm, tips = proper,
            color=red, dashed,thick,domain=-6:0] 
            ({x/\a + (\xTwoInitPosToZeroThree/\a - 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitPosToZeroThree}, {1/\a + (\xTwoInitPosToZeroThree - 1/\a)*exp(-\a*x)});
            \addplot[->,>=latex, color=red, arrow marks=1cm, tips = proper, dashed,thick,domain=0:\zeroControlPosToNegThree] ({(\xTwoInitPosToZeroThree/\a)*(1 - exp(-\a*x)) + \xOneInitPosToZeroThree}, {\xTwoInitPosToZeroThree*exp(-\a*x)});%3 Pos

            %Blue path G
            \addplot[name path=G,draw=none,domain=0:-6] 
            ({-x/\a + (\xTwoInitNegToZeroOne/\a + 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitNegToZeroOne}, {-1/\a + (\xTwoInitNegToZeroOne + 1/\a)*exp(-\a*x)}) -- ++(15cm,0);
            \addplot[->,>=latex,arrow marks=1cm, tips = proper,
            color=blue, dashed,thick,domain=-6:0] 
            ({-x/\a + (\xTwoInitNegToZeroOne/\a + 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitNegToZeroOne}, {-1/\a + (\xTwoInitNegToZeroOne + 1/\a)*exp(-\a*x)});
            %complement
            \addplot[name path=G2,draw=none,domain=0:\zeroControlNegToPosOne] ({(\xTwoInitNegToZeroOne/\a)*(1 - exp(-\a*x)) + \xOneInitNegToZeroOne}, {\xTwoInitNegToZeroOne*exp(-\a*x)});%1 Neg
            \addplot[->,>=latex, color=blue, tips = proper, dashed,thick,domain=0:\zeroControlNegToPosOne] ({(\xTwoInitNegToZeroOne/\a)*(1 - exp(-\a*x)) + \xOneInitNegToZeroOne}, {\xTwoInitNegToZeroOne*exp(-\a*x)});%1 Neg

            %Blue path H
            \addplot[name path=H,draw=none,domain=-6:0]({-x/\a + (\xTwoInitNegToZeroTwo/\a + 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitNegToZeroTwo}, {-1/\a + (\xTwoInitNegToZeroTwo + 1/\a)*exp(-\a*x)});
            \addplot[->,>=latex,arrow marks=1cm, tips = proper,
            color=blue, dashed,thick,domain=-6:0] 
            ({-x/\a + (\xTwoInitNegToZeroTwo/\a + 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitNegToZeroTwo}, {-1/\a + (\xTwoInitNegToZeroTwo + 1/\a)*exp(-\a*x)});
            %complement
            \addplot[name path=H2,draw=none,domain=0:\zeroControlNegToPosTwo] ({(\xTwoInitNegToZeroTwo/\a)*(1 - exp(-\a*x)) + \xOneInitNegToZeroTwo}, {\xTwoInitNegToZeroTwo*exp(-\a*x)});%2 Neg
            \addplot[->,>=latex, color=blue, tips = proper, dashed,thick,domain=0:\zeroControlNegToPosTwo] ({(\xTwoInitNegToZeroTwo/\a)*(1 - exp(-\a*x)) + \xOneInitNegToZeroTwo}, {\xTwoInitNegToZeroTwo*exp(-\a*x)});%2 Neg
            %Fill between path G and H 
            \addplot[blue,fill opacity=0.2]fill between[of=G and H];
            \addplot[blue,fill opacity=0.2]fill between[of=G2 and H2];

            \addplot[->,>=latex,arrow marks=1cm, tips = proper,
            color=blue, dashed,thick,domain=-6:0] 
            ({-x/\a + (\xTwoInitNegToZeroThree/\a + 1/(\a^2))*(1 - exp(-\a*x)) + \xOneInitNegToZeroThree}, {-1/\a + (\xTwoInitNegToZeroThree + 1/\a)*exp(-\a*x)});
            \addplot[->,>=latex, color=blue, arrow marks = 1cm, tips = proper, dashed,thick,domain=0:\zeroControlNegToPosThree] ({(\xTwoInitNegToZeroThree/\a)*(1 - exp(-\a*x)) + \xOneInitNegToZeroThree}, {\xTwoInitNegToZeroThree*exp(-\a*x)});%3 Neg
            \end{axis}
            \end{tikzpicture}
        \end{adjustwidth} 
        \caption{Optimal control trajectories for Problem 4 for $a = 0.5$ and $\lambda = 5$. The solid plot is the final switching curve, the dotted plot is the switching curve to ``off" mode, while the dashed plots are the state trajectories that are not originally on the switching curve.}
    \end{figure}
\end{document}