Abstract
where the drift vector field X an infinitesimal automorphism of G, i.e. the one parameter group of X is a subgroup of Aut(G), the Lie group of automorphisms of G.And the control vector fields yi,j = 1,2, ... k are elements of the Lie algebra L(G) of G, i.e. are right-invariant vector fields on G, hE Hom(G,G 1 ).For this class of systems we establish without proof the following results:1) The Lie algebra rank condition characterizes transitivity, [2].2) The rank condition; it is sufficient for controllability, [2].In particular, we extend the Kalman's Theorem: 3) The rank condition characterizes controllability when G is an Abelian connected Lie group, [2].4) The observability rank condition characterizes the local observability, [1]
Keywords
Controllability
Mathematics
Observability
Lie group
Linear control systems
Linear system
Pure mathematics
Class (philosophy)
Simple Lie group
Discrete mathematics
Algebra over a field
Control theory (sociology)
Control (management)
Computer science
Applied mathematics
Mathematical analysis
Artificial intelligence
Subject Areas
Control and Dynamics of Mobile Robots
·Control and Systems Engineering ·Physical Sciences
Advanced Differential Geometry Research
·Astronomy and Astrophysics ·Physical Sciences
Target Tracking and Data Fusion in Sensor Networks
·Artificial Intelligence ·Physical Sciences
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