一.分段公式等号对齐

\begin{equation}
\left\{
\begin{aligned}
%\nonumber
dx(t)&=[Ax(t-\delta)+Bu(t)+Cw(t)]dt +DdW(t), t\in(0,T],\\
x(s)&=\xi(s), s\in [-\delta, 0].\\
\end{aligned}
\right.
\end{equation}

&起对齐作用,等于号=处对齐。如果不想标号, 将%\nonumber前面%去掉即可。
形式如下

二.有目标函数的分段公式对齐

\begin{align}
\nonumber
&min_{u\in \mathcal{U}}J_1(u(\cdot), w(\cdot))\\
&s.t.\left\{
\begin{aligned}
%\nonumber
dx(t)&=[Ax(t-\delta)+Bu(t)+Cw(t)]dt +DdW(t), t\in(0,T],\\
x(s)&=\xi(s), s\in [-\delta, 0].\\
\end{aligned}
\right.
\end{align}

&起对齐作用, 此处有两处对齐, min和s.t.对齐, 等于号对齐。如果不想标号, 将%\nonumber前面%去掉即可。
形式如下

三.分段公式内部分段的对齐

\begin{equation}
\left\{
\begin{aligned}
%\nonumber
V_1(t,x_t)=&P_0(t)x^2(t)+2P_1(t)x(t)w(t)+P_2(t)w^2(t)+P_3(t)\\
&+2x(t)\int_{t-\delta}^tQ_0(t,\tau-t)x(\tau)d\tau\\
&+2w(t)\int_{t-\delta}^tQ_1(t,\tau-t)x(\tau)d\tau\\
&+\int_{t-\delta}^t\int_{t-\delta}^tx(\tau)x(s)R(t,s-t,\tau-t)d\tau ds,t\in[0,T),\\
V_1(T,x_T)=&H_1x^2(T).\\
\end{aligned}
\right.
\end{equation}

&起对齐作用,等于号=后面的第一个字母和+对齐。如果不想标号, 将%\nonumber前面%去掉即可。
形式如下

四.公式内部分段的对齐

\begin{align*}
&E[V_1(T,x_T)-V_1(0,x_0)]+E\{\int_0^T[M_1x^2(t)+N_1u^2(t)]dt\}\nonumber\\
=&E\{\int_0^T[M_1x^2(t)+N_1u^2(t)]dt+H_1x^2(T)\}-V_1(0,x_0)\\
=&E\{\int_0^T[B_1P^2_0(t)x^2(t)+B_1P^2_1(t)w^2(t)+2B_1P_0(t)P_1(t)x(t)w(t)\\
&+2B_1P_0(t)x(t)\int_{t-\delta}^tx(\tau)Q_0(t,\tau-t)d\tau+2B_1P_1(t)w(t)\int_{t-\delta}^tx(\tau)Q_0(t,\tau-t)d\tau\\
&+B_1\int_{t-\delta}^t\int_{t-\delta}^tx(\tau)x(s)Q_0(t,\tau-t)Q_0(t,s-t)d\tau ds\\
&+2Bu(t)(P_0(t)x(t)+P_1(t)w(t)+\int_{t-\delta}^tQ_0(t,\tau-t)x(\tau)d\tau)+N_1u^2(t)]dt\}\\
=&E\{\int_0^TN_1[u(t)+N^{-1}_1B(P_0(t)x(t)+P_1(t)w(t)+\int_{t-\delta}^tQ_0(t,\tau-t)x(\tau)d\tau)]^2dt\}\\
\geq&0.
\end{align*}

五.分段公式内部公式过长分行的对齐

\begin{align}
\left\{
\begin{aligned}
%\nonumber
&\dot{I}_0(t)+2I_1(t,0)-2B_1P_0(t)I_0(t)+M_2-B_2I^2_0(t)=0,\\
&B_2I_0(t)I_1(t,\tau)=
\begin{aligned}[t]
&(\frac{\partial}{\partial t}-\frac{\partial}{\partial \tau})I_1(t,\tau)+I_2(t,\tau,0)-B_1P_0(t)I_1(t,\tau)\\
&-B_1I_0(t)Q_0(t,\tau),\\
\end{aligned}\\
&(\frac{\partial}{\partial t}-\frac{\partial}{\partial \tau}-\frac{\partial}{\partial s})I_2(t,\tau,s)-2B_1Q_0(t,s)I_1(t,\tau)-B_2I_1(t,\tau)I_1(t,s)=0,\\
&\dot{I}_3(t)+D^2I_0(t)=0.\\
\end{aligned}
\right.
\end{align}

&起对齐作用,所有公式左对齐,大括号里面最长的公式另起aligned环境,等于号后面和下一行公式对齐。如果不想标号, 将%\nonumber前面%去掉即可。
形式如下

\

\begin{align}
\left\{
\begin{aligned}
%\nonumber
&(\frac{\partial}{\partial t}-\frac{\partial}{\partial \tau})Q^{(k)}_0(t,\tau)=
\begin{aligned}[t]
&B_1P^{(k)}_0(t)Q^{(k-1)}_0(t,\tau)+B_1P^{(k-1)}_0(t)Q^{(k)}_0(t,\tau)\\
&-R^{(k)}(t,0,\tau)-B_1P^{(k-1)}_0(t)Q^{(k-1)}_0(t,\tau),\\
\end{aligned}\\
&(\frac{\partial}{\partial t}-\frac{\partial}{\partial \tau})Q^{(k)}_1(t,\tau)=
\begin{aligned}[t]
&B_1P^{(k)}_1(t)Q^{(k-1)}_0(t,\tau)+B_1P^{(k-1)}_1(t)Q^{(k)}_0(t,\tau)\\
&-CQ^{(k)}_0(t,\tau)-B_1P^{(k-1)}_1(t)Q^{(k-1)}_0(t,\tau),\\
\end{aligned}\\
&(\frac{\partial}{\partial t}-\frac{\partial}{\partial s}-\frac{\partial}{\partial \tau})R^{(k)}(t,s,\tau)=
\begin{aligned}[t]
&B_1Q^{(k-1)}_0(t,\tau)Q^{(k)}_0(t,s)\\
&-B_1Q^{(k-1)}_0(t,\tau)Q^{(k-1)}_0(t,s)\\
&+B_1Q^{(k)}_0(t,\tau)Q^{(k-1)}_0(t,s).\\
\end{aligned}
\end{aligned}
\right.
\end{align}

&起对齐作用,所有公式左对齐,大括号里面最长的公式另起aligned环境,等于号后面和下一行公式对齐。如果不想标号, 将%\nonumber前面%去掉即可。
形式如下

注： 其余数学公式可以查看该链接Mathmode - v.2.47