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Singularities of discontinuous dynamical systems. (Russian) Zbl 1074.93526

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.

MSC:

93C10 Nonlinear systems in control theory
70H25 Hamilton’s principle
49K15 Optimality conditions for problems involving ordinary differential equations
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