Greedy optimal control

For discrete-time control-affine systems on an infinite interval, an analytical solution of the greedy optimal control problem is presented. The "greedy" formulation of the optimal control problem calls for minimization of the instantaneous cost function, rather than the cumulative one, as in the conventional optimal control. For a class of linear discrete-time systems a relation between greedy and conventional optimal controls is established. For nonlinear control-affine systems, sufficient conditions for asymptotic stability under the greedy optimal control are given.