Control Processes Research Center of Program Systems Institute of RAS conducts researches in the field of mathematical control theory and its applications. Geometrical, analytical and computer methods for detailed analysis of nonlinear control problems with big symmetry group are developed (in particular, invariant problems on Lie groups and homogeneous spaces). An important research direction of the center is applying obtained theoretical results to solve actual problems in image restoration, mechanics and robotics.
Yuri L. Sachkov, Doctor of Sciences in Mathematics, is the chief of the Center.
Main research areas:
- Invariant optimal control problems on Lie groups,
- Sub-Riemannian and Riemannian geometry on Lie groups,
- Sub-Lorentzian geometry on Lie groups,
- Almost-Riemannian geometry,
- Methods for solving singularly perturbed control problems,
- Applications of the theory of functions to control problems,
- Controllability of invariant systems on Lie groups,
- Controllability of bilinear systems
- Constructive methods for solving two-point control problems,
- Recovery and processing of damaged images,
- Movement of mobile robots with trailers,
- Euler elasticae,
- Rolling solids,
- Algorithms and programs, including parallel ones, for the approximate solution of control problems.