Controllability of differential systems with variable structure and the recovery problem

The talk is devoted to the study of controllability of differential systems of variable structure and the problem of optimal recovery of the solution of a linear system of ordinary differential equations from the initial information with random error. New results for different classes of nonlinear systems are obtained. A sufficient condition of controllability of nonlinear triangular differential systems in the problem with phase space change is proved. A sufficient condition of controllability of the system with phase space change in the case when the right parts of differential inclusions are concave mappings is proved. A sufficient condition of controllability of the problem with phase space change is proved in the case when the nonlinear system in the first space is linearised at some replacement of variables, and the nonlinear system in the second space is locally zero-controllable. The theorems on the optimal recovery of the linear operator and the solution of the linear system of differential equations by the initial information with random error are proved. The solution of the system of ordinary differential equations is recovered under different variants of the initial information.