Optimal Control Problems on Lie groups

Abstract

Optimal control problems on a Lie group G make an interesting link between modern control theory and its classical past through the problems of elastica [6], and its geometric counterpart the problem of Radon ([1]). The first of these problems consists of minimizing $\frac{1} {2}\int_0^\ell {\left( {{C_1}u_1^2 + {C_2}u_2^2 + {C_3}u_3^2} \right)dt}$ over the trajectories g(t) in the group of motions of R ³ which satisfy.