Problems in Geodesic Control

Abstract

In recent papers [2,4,10,11] we have seen control systems defined on Lie groups. That is, if G is a Lie group, L(G) its Lie algebra of right invariant vector fields, then systems of the form

$$ {{dx} \over {dt}}(t) = {x_0}(x(t)) + \sum\limits_{i = 1}^m {{u_i}} (t) {x_i}(x(t)) $$

X_o,...., X_m are in L(G) and x(t) is in G, have been studied. The problems of realisation, observability, [2], to some extent optimality, [l0] , and in particular controllability, [2,4,ll] have been investigated.