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Summary
Control Processes Research Center of Program Systems Institute of RAS conducts research 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.
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 boundary value control problems;
- Recovery and processing of damaged images;
- Movement of mobile robots with trailers;
- Euler's elasticae;
- Rolling solids;
- Algorithms and programs, including parallel ones, for the approximate solution to control problems.
Main Results
Difficult actual problems of the geometric control theory were studied:
- Euler's elastic problem;
- The problem of optimal rolling of a sphere on a plane without slipping;
- Sub-Riemannian problems on Lie groups: SE(2), SH(2), SO(3), Engel group and Cartan group.
Algorithms and software for solving
- motion planning problem for mobile robot with trailers on a plane as well as for sphere rolling on a plane;
- image restoration problem (using human brain inspired method).
Presentation Data
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