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A. Steindl:
"Invariant manifolds in control problems";
PAMM, 19 (2019), 1; 4 S.

Invariant manifolds are useful tools for the investigation of nearly all nonlinear systems. Especially for the determination of stabilizing controls the center‐stable manifold characterizes the proper feedback controls.

The method is demonstrated for the stabilization of a tethered satellite in the local vertical position by applying tension control. While in‐plane perturbations can be extinguished in finite time, the tension control acts as parametric excitation for out‐of‐plane perturbations and is only able to cause a slow algebraic decay for both kinds of perturbations. An analytical or numerical power series expansion of the center‐stable manifold at the target state provides the proper feedback controls.

Invariant Manifolds; Normal Form reduction; optimal control; tethered satellites

http://dx.doi.org/10.1002/pamm.201900479

https://doi.org/10.1002/pamm.201900479