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We consider the trajectory tracking problem for a dynamical system described by nonlinear fractional differential equations with an unknown input disturbance. Based on regularization methods and constructions from guaranteed positional control theory, we propose an information noise- and computational error-robust algorithm solving the problem for the case in which only part of the system parameters can be measured.

For a controlled dynamical system described by nonlinear fractional differential equations, we consider the problem of dynamic reconstruction of an unknown disturbance from approximate measurements of the trajectory. For this problem, we construct an algorithm based on Krasovskii's extremal shift method and find its convergence rate.

A game control problem for a parabolic differential equation with memory is considered. An algorithm for its solution based on Krasovskii’s method of extreme shift and the method of stable paths is proposed.

We consider the trajectory tracking problem for a dynamical system described by a parabolic differential equation with memory. We present an algorithm for solving this problem based on the Krasovskii extremal shift method.

For a nonautonomous system of linear advanced differential equations, we find asymptotic formulas analytically determining how the regular solutions of this system on an interval of the positive half-line depend on the admissible error. The problem is solved in the following setting: additional smoothness conditions are imposed on the initial functions, but the boundary conditions providing a continuous extension of the solutions of the Cauchy problem to an interval of the positive half-line are violated.

We consider unique determination and right uniqueness issues for solutions, satisfying the one-sided Lipschitz condition, of functional-differential equations with discontinuous right-hand side.