Stabilization and Analytic Approximate Solutions of an Optimal Control Problem

This paper analyses a dynamical system derived from a left-invariant, drift-free optimal control problem on the Lie group SO(3) x R-3 x R-3 in deep connection with the important role of the Lie groups in tackling the various problems occurring in physics, mathematics, engineering and economic areas [1-5]. The stability results for the initial dynamics were inconclusive for a lot of equilibrium points (see [6]), so a linear control has been considered in order to stabilize the dynamics. The analytic approximate solutions of the resulting nonlinear system are established and a comparison with the numerical results obtained via the fourth-order Runge-Kutta method is achieved.