The research of the department of General Problems of Control has taken four major directions, each of which has several branches. Let us name them.

1. Theory of extremal problems and problems of analysis:

• general Lagrange principle, problems of convex analysis and methods of duality in the theory of extremal problems
  
  (V.M. Tikhomirov, G.G. Magaril-Ilyayev);
• best approximation of functional classes and finite-dimensional sets; embedding theorems, widths theory
  (V.M. Tikhomirov, E.M. Galeev, S.V. Konyagin, G.G Magaril-Ilyayev, K.Yu. Osipenko, A.S. Kochurov, A.A. Vasilyeva);
• function approximation
  (V.M. Tikhomirov, S.V. Konyagin, E.M. Galeev, G.G. Magaril-Ilyayev, V.B. Demidovich, A.S. Kochurov, A.V. Rozhdestvenskiy, V.Yu. Protasov, K.S. Ryutin);
• spline theory
  (V.M. Tikhomirov, G.G. Magaril-Ilyayev, V.Yu. Protasov, V.B. Demidovich, D.A. Silayev, A.S. Kochurov);
• wavelet analysis
  (S.V. Konyagin, V.Yu. Protasov);
• extremal properties of classical and generalized polynomials
  (V.M. Tikhomirov, G.G. Magaril-Ilyayev, S.V. Konyagin, V.B. Demidovich);
• geometry of Banach spaces
  (S.V. Konyagin);
• harmonic analysis and its applications in number theory
  (S.V. Konyagin);
• estimations of pseudo-dimensionality of family of functions
  (K.S. Ryutin).

2. Optimal control and ordinary differential equations:

• general theory of optimal control
  (V.M. Tikhomirov, M.I. Zelikin, A.V. Fursikov, A.V. Dmitruk, N.P. Osmolovskiy);
• optimal synthesis with chattering
  (M.I. Zelikin, L.V. Locutsievsiy);
• homogeneous spaces and Riccati differential equations
  (M.I. Zelikin);
• differential games
  (M.I. Zelikin, L.V. Locutsievskiy);
• qualitative theory of differential and finite-difference equations
  (M.I. Zelikin, A.G. Kushnirenko, V.B. Demidovich, L.V. Locutsievskiy);
• ergodic properties of dynamic systems
  (A.V. Rozhdestvenskiy, L.V. Locutsievskiy);
• controllability and observability of dynamic systems
  (E.Ya. Roytenberg).

3. Optimal control and partial differential equations:

• general theory of boundary problems for partial differential equations
  (A.V. Fursikov);
• minimization of multiple integrals
  (M.I. Zelikin);
• controllability of systems with distributed parameters
  (A.V. Fursikov, A.V. Gorshkov);
• statistical hydromechanics
  (A.V. Fursikov);
• systems of Navier-Stokes equations
  (A.V. Fursikov, A.V. Gorshkov);
• pseudo-differential operators
  (A.S. Demidov);
• asymptotic behavior of solutions of systems with a small parameter
  (A.S. Demidov);
• boundary layer theory
  (D.A. Silayev);
• free-boundary problems
  (A.S. Demidov).

4. Optimization, optimal control, numerical methods and questions of applied mathematics:

• problems of hydrodynamics, electrodynamics and plasma theory
  (D.A. Silayev, A.S. Demidov);
• optimal control in mathematical economics
  (M.I. Zelikin, L.V. Lokutsiyevskiy);
• optimal control in dynamics of space flights
  (M.P. Zapletin, D.A. Silayev);
• optimization in actuarial and financial mathematics
  (V.B. Demidovich, A.S. Kochurov, A.V. Rozhdestvenskiy, V.Yu. Protasov, K.S. Ryutin);
• numerical methods based on the theory of Chebyshev generalized polynomials
  (V.B. Demidovich);
• calculation of widths and information coding
  (A.S. Kochurov);
• system programming and computer support of educational process
  (A.G. Kushnirenko).