Optimal Sampling Pattern for the Free Final Time Linear Quadratic Regulator

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