# Optimal Control

Consider the optimal control problem with an optimal trajectory $x^*(t)$ and an initial point $(x_1^0,x_2^0)$ $$\begin{split} \dot{x}=A x + Bu \\\ J=\int^\infty_0(x_2^2+\epsilon u^2)dt \end{split}$$ whera $(A,B)$ is minimal. How do I analyze $\lim_{\epsilon\rightarrow 0}x^*(t)$?

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