Fuller's phenomenon: review
The Fullers phenomenon consists of the presence of an infinite number of switching points of the optimal control on a finite time interval (a chattering arc). The article provides an extensive and up-to-date review of the results related to Fullers phenomenon in optimal control theory. Starting with the original linear-quadratic two-dimensional problem considered by Fuller in early 1960s, the author proceeds to a series of works where linear-quadratic problems with chattering optimal regimes were studied in higher dimensions. It is mentioned that a qualitative picture of the optimal feedback synthesis in a Fuller problem of dimension higher than three still remains an open problem. Then, the appearance of chattering optimal controls at the transition from regular to singular regime of an extremal is discussed. In the end, recent general results about the Lagrangian manifolds of chattering extremals and the co-dimension of the singularities of a discontinuous Hamiltonian system are presented. A substantial part of the review is based on the works by \textit{M. I. Zelikin} and the author [see, e.g., ``Theory of chattering control with applications to astronautics, robotics, economics, and engineering'' (1994; Zbl 0820.70003)].
scientific article; zbMATH DE number 1526531
scientific article