ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 93, 17 Sachkov, Yuri L., Program Systems Institute, Pereslavl-Zalessky, Russia Controllability of right-invariant systems on solvable Lie groups A right-invariant control system ẋ = A(x)+∑_{i=1}^{m} u_{i}B_{i}(x) on a Lie group G is called controllable if any two points in the group G can be connected by a trajectory of the system. We are interested in conditions of controllability of such systems in terms of the Lie group G, its Lie algebra L, and the rightinvariant vector fields A, B_{1}, …, B_{m} ∈ L. For simply connected Lie groups G ≠ [G, G] we give necessary and sufficient controllability conditions close one to another. For dim G ≤ 6 almost complete classification of controllable single-input (m = 1) systems is given. Ref. Yu. L. Sachkov, Controllability of Hypersurface and Solvable Invariant Systems, Journal of Dynamical and Control Systems 2 (1996), 1: 55–67. Yu. L. Sachkov, Controllability of Right-Invariant Systems on Solvable Lie Groups, Journal of Dynamical and Control Systems, 3 (1997), 4: 531–564. Yu. L. Sachkov, Controllability of Right-Invariant Systems on Solvable Lie Groups: a Survey and Some New Results, Proc. of the AMS Summer Research Inst. on Differential Geometry and Control, Boulder, USA, July 1997, accepted.