Pukhlikov, A. V. Singularities of discontinuous dynamical systems. (Russian) Zbl 1074.93526 Dokl. Akad. Nauk, Ross. Akad. Nauk 378, No. 4, 456-458 (2001). The goal is to describe critical elements (here: singular subsets and singular trajectories) of discontinuous dynamical systems. According to the Pontryagin maximum principle, the problem of optimal control of a dynamic system \(\frac{dx}{dt} = f(x,u)\), \(x \in X\), \(u \in U\) is reduced to studies of integral trajectories of a corresponding discontinuous Hamiltonian system \(s\operatorname{grad}H\) evolving in the cotangent bundle of the configuration space. Reviewer: Andrei Zemskov (Moskva) MSC: 93C10 Nonlinear systems in control theory 70H25 Hamilton’s principle 49K15 Optimality conditions for problems involving ordinary differential equations Keywords:optimal control; singularity; Pontryagin’s principle; PoincarĂ© congruence; discontinuous systems; bundle; cotangent PDFBibTeX XMLCite \textit{A. V. Pukhlikov}, Dokl. Akad. Nauk, Ross. Akad. Nauk 378, No. 4, 456--458 (2001; Zbl 1074.93526)