Abstract:
For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.
Citation:
V. F. Borisov, M. I. Zelikin, L. A. Manita, “Optimal synthesis in an infinite-dimensional space”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 40–58; Proc. Steklov Inst. Math., 271 (2010), 34–52