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\documentclass[ngerman]{scrartcl}
\usepackage[T1]{fontenc}
\usepackage{selinput}
\SelectInputMappings{    % Ersatz für »inputenc« aus dem Bündel »oberdiek«
  adieresis={ä},
  germandbls={ß}
}
\usepackage{babel}
\usepackage{mathtools}   % lädt »amsmath« und bietet Verbesserungen

\begin{document}
  \begin{subequations}\label{ocp:simple}
    \begin{alignat}{3}
      \min_{x,u} \mathrlap{\int_{0}^{1} \Phi\left(t,x(t),u(t)\right) \,\text{d}t} \\
      \text{s.\ t.} &  
       & \dot{x}(t) &= f\big(t,x(t),u(t)\big), \qquad & t \in [0,1]\\
      && \sum\limits_{j=0}^Mr_j\big(x(t_j)\big) &= 0 \\
      &&\qquad g\big(t,x(t),u(t)\big) &\geq 0 , & t \in [0,1] \label{ocp:simple:pathcon}
    \end{alignat}
  \end{subequations}
\end{document}

\documentclass[a4paper, 12pt]{scrreprt}

\usepackage{amsmath}

\begin{document}
\begin{subequations} \label{ocp:simple}
	\begin{align}
	\underset{x, u }{\text{min}}  & \int_{0}^{1} \Phi(t, x(t), u(t)) dt  \\
	\text{s.t.}&	
	\begin{aligned}[t]
			 	\dot{x}(t) &= f(t,x(t),u(t)), & t \in \left[0,1 \right] \\
				\sum\limits_{j=0}^Mr_j(x(t_j)) &= 0& \\
				g(t,x(t),u(t)) & \geq 0 , & t \in \left[0, 1 \right] \label{ocp:simple:pathcon}
	\end{aligned}
	\end{align}
\end{subequations}
\end{document}

\begin{subequations} \label{ocp:simple}
	\begin{align}
	\underset{x, u }{\text{min}}  & \int_{0}^{1} \Phi(t, x(t), u(t)) dt  \\
	\text{s.t.}&	
	\begin{aligned}[t]
			 	\dot{x}(t) &= f(t,x(t),u(t)), & t \in \left[0,1 \right] \\
				\sum\limits_{j=0}^Mr_j(x(t_j)) &= 0& \\
				g(t,x(t),u(t)) & \geq 0 , & t \in \left[0, 1 \right] \label{ocp:simple:pathcon}
	\end{aligned}
	\end{align}
\end{subequations}