- Convex and applied nonlinear analysis, theory of set-valued mappings, Aumann’s integral, measurable structures
- Mathematical theory of optimal control, differential inclusions, complete conflict controllability
- Game problems for discrete systems, Pontryagin’s direct methods, semigroup operators of Pshenicnyi
- Theory of search for moving objects, stochastic dynamic games
- Differential games of pursuit and evasion, nonlinear problems on moving objects collision avoidance
- Evolutionary game problems
- Game problems for systems of integral, integral-differential and differential-difference equations
- Dynamic games with groups of participants. Group pursuit, pursuit in turn (dynamic “commercial traveler” problem), game problems under state constraints
- Systems with impulse control, integral and mixed constraints on control
- Game problems for systems with fractional derivatives of Riemann – Liouville, Dzharbasyan – Nersesyan – Caputo, Miller – Ross, Hilfer, Gryunvald – Letnikov
- Investigation of the method of resolving functions, upper and lower resolving functions, matrix resolving functions, choice of extremal selections
- Positional methods in game problems, generalization of the Krasovskii extremal targeting rule, Pontryagin’s maximum principle
- Dynamic systems of variable structure, hybrid systems, failure of controlling devices
- Game problems for systems with distributed parameters
- Methods of the theory of making decision, artificial intelligence and system analysis
- Systems of control by spacecrafts and systems of search for sea objects
- Exploration of functional human possibilities in extreme conditions
- Modeling of sport single combating, competition of firms
- Aircraft control systems, soft landing
