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Invariant manifolds in control problems
Author(s) -
Steindl Alois
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900479
Subject(s) - center manifold , invariant manifold , control theory (sociology) , nonlinear system , invariant (physics) , parametric statistics , manifold (fluid mechanics) , algebraic number , mathematics , mathematical analysis , physics , computer science , control (management) , engineering , artificial intelligence , mathematical physics , mechanical engineering , statistics , hopf bifurcation , quantum mechanics , bifurcation
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.