Abstract
A systematic research on the structure-preserving controller is investigated in this paper, including its applications to the second-order, first-order, time-periodic, or degenerated astrodynamics, respectively. The general form of the controller is deduced for the typical Hamiltonian system in full feedback and position-only feedback modes, which is successful in changing the hyperbolic equilibrium to an elliptic one. With the poles assigned at any different positions on imaginary axis, the controlled Hamiltonian system is Lyapunov stable. The Floquet multiplier is employed to measure the stability of time-dependent Hamiltonian system, because the equilibrium of periodic system may be unstable even though the equilibrium is always elliptic. One type of periodic orbits is achieved by the resonant conditions of control gains, and another type is making judicious choice in the foundational motions with different frequencies. The control gains are selected from the viewpoint of both the local and global optimizations on fuel cost. This controller is applied to some astrodynamics to achieve some interesting conclusions, including stable lissajous orbits in solar sail’s three-body problem and degenerated two-body problem, quasiperiodic formation flying on aJ2-perturbed mean circular orbit, and controlled frozen orbits for a spacecraft with a high area-to-mass ratio.
Highlights
It is well known that most of the astrodynamical problems could be classified as hyperbolic Hamiltonian systems, for example, circular restricted 3-body problem (CR3BP)
The control gains are selected from the viewpoint of both the local and global optimizations on fuel cost. This controller is applied to some astrodynamics to achieve some interesting conclusions, including stable lissajous orbits in solar sail’s three-body problem and degenerated two-body problem, quasiperiodic formation flying on a J2-perturbed mean circular orbit, and controlled frozen orbits for a spacecraft with a high area-to-mass ratio
This paper proposes a structure-preserving controller to generate bounded trajectories around the equilibrium, which has many potential applications in astrodynamics
Summary
It is well known that most of the astrodynamical problems could be classified as hyperbolic Hamiltonian systems, for example, circular restricted 3-body problem (CR3BP). Further work was implemented on the stabilization of the equilibrium for time-periodic system, which has time varying topological types and no fixed-dimensional unstable/stable/center manifolds [6]. The controller is successful in changing the hyperbolic equilibrium (saddle) to an elliptic one (center) with the poles on the imaginary axis (marginal stability), and the controlled Hamiltonian system can achieve the Lyapunov stability by means of the Morse lemma. Some selection techniques on the gains are considered from the point view of both the local and global optimizations This controller is applied to some astrodynamics to achieve some interesting conclusions, including stable lissajous orbits in solar sail’s three-body problem and degenerated two-body problem, quasiperiodic formation flying on a J2-perturbed mean circular orbit, controlled frozen orbits for a spacecraft with high area-to-mass ratio
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