Periodic near optimal control
In this very important and useful paper, the finite time optimal control problem of minimizing an average cost functional for nonlinear singularly perturbed systems is considered. The problem of the existence of near optimal trajectories which are periodic is proposed. For this purpose nonlinear control systems with three time scales are investigated and a limiting system for the slowest motion is constructed by an iterated averaging procedure. Main result: The author shows that global tools, invariant control sets, and local tools, Lie algebra ranks of vector fields are presented under singular perturbations. The existence of periodic near optimal trajectories is verified under the condition that the fast subsystem and an unperturbed slow subsystem are controllable and that a standard Lie algebra rank condition for local accessibility holds.
scientific article; zbMATH DE number 1506523
scientific article