On an optimal flow in a class of nilpotent convex problems
- 15 Downloads
A comprehensive analysis of optimal synthesis is carried out for a class of nilpotent convex problems with multidimensional control. It is shown that the synthesis of optimal trajectories forms a nonsmooth half-flow (which is reasonably called optimal) in the state space. An optimal solution starting at some point of the state space is the trajectory of this point under the action of the optimal flow. The existence of an optimal flow entails many important corollaries. For example, applying the Cantor–Bendixson theorem, one can prove that an optimal control in nilpotent convex problems may have at most a countable number of discontinuity points.
KeywordsSTEKLOV Institute Optimal Trajectory Quotient Space Countable Number Discontinuity Point
Unable to display preview. Download preview PDF.
- 5.M. I. Zelikin, L. V. Lokutsievskiy, and R. Hildebrand, “Geometry of neighborhoods of singular trajectories in problems with multidimensional control,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 277, 74–90 (2012) [Proc. Steklov Inst. Math. 277, 67–83 (2012)].Google Scholar
- 6.M. I. Zelikin, L. V. Lokutsievskiy, and R. Hildebrand, “Typicalness of chaotic fractal behaviour of integral vortexes in Hamiltonian systems with discontinuous right hand side,” Sovrem. Mat., Fundam. Napr. 56, 5–128 (2015); arXiv: 1506.02320 [math.DS].Google Scholar