I was given the state space equation, $\dot{x} = -2x + u$ and told to determine the optimal control law $u=-kx$ which minimizes the performance index
$$J = \int_{0}^{\infty} x^{2}\,dt.$$
My approach was to find the state feedback $k$. But since the value of $R$ (positive definite Hermitian) is not given. That means $R=0$. How do I determine the optimal control for this system where $R=0$?