Differential equations that contain singular manifolds, in control and minimization problemsстатья
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Дата последнего поиска статьи во внешних источниках: 27 мая 2015 г.
Аннотация:The paper deals with the n-dimensional system of differential equations z ˙=F(z,y), z(0)=z 0 , containing singular manifolds (attracting or semi-attracting) on which the right-hand sides of the equations become infinite. These manifolds are used in constructing penalty functions while solving the problem of conditional extremum of a function by means of gradient methods. Analogously, this approach is also used for solving the control problem x ˙=f(x,u) under some constraints on phase variables in the class of piecewise smooth functions. In conclusion, the author develops a numerical algorithm for integration of a differential system that reaches its singular manifold.