Optimal Sampling Pattern for the Free Final Time Linear Quadratic Regulator

The optimal sampling problem is the selection of instants together with control actions such that a given cost function minimized. In this article, we solve for free final time linear quadratic regulator. Each instant computed as minimization maximum eigenvalue formulated at each stage by previously applying dynamic programming. solution provides instants, actions, and in recursive constructive way. Furthermore, any arbitrary number moves $N \geq 1$ , it not based on asymptotic arguments. Two application examples show feasibility approach.