Stabilization and Analytic Approximate Solutions of an Optimal Control Problem
Abstract
This paper analyses a dynamical system derived from a left-invariant, drift-free optimal control problem on the Lie group SO(3) × &R;3 × &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 [<xref ref-type="bibr" rid="j_phys-2018-0064_ref_001">1</xref>, <xref ref-type="bibr" rid="j_phys-2018-0064_ref_002">2</xref>, <xref ref-type="bibr" rid="j_phys-2018-0064_ref_003">3</xref>, <xref ref-type="bibr" rid="j_phys-2018-0064_ref_004">4</xref>, <xref ref-type="bibr" rid="j_phys-2018-0064_ref_005">5</xref>]. The stability results for the initial dynamics were inconclusive for a lot of equilibrium points (see [<xref ref-type="bibr" rid="j_phys-2018-0064_ref_006">6</xref>]), 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.
- Publication:
-
Open Physics
- Pub Date:
- August 2018
- DOI:
- 10.1515/phys-2018-0064
- Bibcode:
- 2018OPhy...16...64P
- Keywords:
-
- ordinary differential equations;
- solution of equations;
- optimal control;
- nonlinear stability;
- optimal homotopy asymptotic method