Mathematical control theory
- Mapping nonlinear controlled systems to linear ones
- Min-moment problem and solution of the time-optimal control problem
- Метод функції керованості
- Mapping trajectories of nonlinear controlled systems to trajectories of linear systems
- Controllability of linear systems with control constraints
- Algebraic methods for studying nonlinear controlled systems
- Homogeneous approximation, methods of its description and construction
- Nonlinear time-optimal control problem
- Nonlinear controlled systems, mapping of nonlinear systems
- Stabilization problem for nonlinear systems in the critical case
- Positional synthesis problem for essentially nonlinear systems
- Stabilization, finite-time stabilization, estimation of motion time
- Controllability of mechanical systems
- Uncertain systems. Synthesis problem for robust systems, robust control
Mathematical biology
- Mathematical modeling in biology and medicine
- Mathematical modeling in ecology
- Optimization methods
- Biomechanics
- Mathematical modeling of liver regeneration processes
- Problem of finding optimal control strategies for liver regeneration processes
Partial Differential Equations
- Control theory
- Qualitative properties of solutions
- Boundary value problems
- Nonlinear partial differential equations
- Qualitative theory of quasilinear parabolic equations
Algebra
- Algebraic properties of implicit differential and difference equations over rings, including over the ring of integers and over the ring of polynomials
- Linear and nonlinear differential equations in modules over commutative rings
- Non-Archimedean topologies, p-adic numbers
Hydrodynamics
- Wave motions, vortices
- Hydrodynamic theory of filtration
Applied interval analysis
- Methods for solving interval equations
- Stability of interval matrices
Data analytics
- Data structures and models
- Databases, information systems
- Structural and semantic data analysis
- Volumetric and cross-domain knowledge