A remark on reachable sets of linear systems
- 1 August 1972
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 17 (4) , 547
- https://doi.org/10.1109/tac.1972.1100062
Abstract
Any compact convex set of R d can occur as a reachable set of some d -dimensional linear differential system with compact control variable constraint set. However, with the constraint sets most frequently considered in the literature, the reachable sets must be zonoids, a severe restriction on possible shapes when d > 2 . On the other hand, given a zonoid, there is a differential system with scalar bang-bang control that has this zonoid as a reachable set.Keywords
This publication has 3 references indexed in Scilit:
- The generalized differential equation ẋ ϵ R(t, x)Advances in Mathematics, 1970
- A class of convex bodiesTransactions of the American Mathematical Society, 1969
- Calculus of Set Valued Functions and ControlIndiana University Mathematics Journal, 1968