Solution Curve For Control Systems on Lie Groups - Softcover

Lima De Oliveira, Joćo Paulo

Softcover

ISBN 10: 6202923938 ISBN 13: 9786202923934

Publisher: LAP Lambert Academic Publishing, 2020

Synopsis

In the context of Lie groups, Control Theory is primarily concerned with the study of invariant, linear, bilinear and affine control systems. For invariant systems - considering that the control functions are piecewise constant - the solutions of the system has a well known and good description. This brings us to the first objective of this work: to give an explicit description of the solution curve for the other systems under the assumption that the linear vector fields commute. These solutions are obtained as the integral curve of a convenient invariant vector field on a semidirect product of a Lie group with an Euclidean space. In particular, we consider the case where the derivations associated to the linear vector fields are inner (which occurs, for example, in every semi simple Lie algebra), in which case the solutions are described in a considerably simpler and more elegant way. Thenceforth, our achievements are applied to obtain new propositions. The results range from expressions that relate the controllability of linear/affine control systems with associated invariant ones to the study of system semiconjugation by Lie group homomorphisms and properties of stability sets.

Edition details

• Publisher: LAP Lambert Academic Publishing
• Publication date: 2020
• ISBN 10: 6202923938
• ISBN 13: 9786202923934
• Binding: Paperback
• Language: English
• Number of pages: 68