Integral representation of trajectories of control systems with generalized right-hand sides.

*(English. Russian original)*Zbl 0674.34064
Differ. Equations 24, No. 9, 1021-1031 (1988); translation from Differ. Uravn.24, No. 9, 1551-1564 (1988).

Consider quasilinear systems of ODES whose right-hand sides contain linearly entering generalized functions as control. A multiplicative analogue of integration by parts is presented for expressing a solution of the differential equation, which is generated by a measurable control, through the primitive of this control. This formula gives the possibility to construct trajectories of the systems linear in the control which are generated by the generalized controls from the spaces \(W_{1,\infty}\) and to prove the continuity of a mapping in some topologies of these spaces. Generalized trajectories of linear and quasilinear systems of differential equations with generalized functions as coefficients are studied.

Reviewer: J.Tian

##### MSC:

34H05 | Control problems involving ordinary differential equations |