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The optimal sampling problem is the selection of the optimal sampling instants together with the optimal control actions such that a given cost function is minimised. In this article, we solve the optimal sampling problem for free final time linear quadratic regulator with scalar dynamical system. The solution provides the optimal sampling instants, control actions and the optimal final time in a recursive and constructive way for any arbitrary number of samples, as it is not based on asymptotic arguments. An application example shows the feasibility of the approach.

Optimal sampling pattern for free final time linear quadratic regulator: the scalar case