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Solving optimal control problems by using inherent dynamical properties
Author(s) -
Flaßkamp Kathrin,
OberBlöbaum Sina,
Kobilarov Marin
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010281
Subject(s) - optimal control , invariant (physics) , nonlinear system , simple (philosophy) , homogeneous space , control theory (sociology) , mathematical optimization , mathematics , computer science , dynamical systems theory , inverted pendulum , control (management) , geometry , physics , artificial intelligence , philosophy , epistemology , quantum mechanics , mathematical physics
We present a technique for computing optimal control trajectories by exploiting the inherent structure of the dynamics arising from symmetries and invariant (un)stable manifolds of fixed points. Our approach is based on sequencing motions along relative equilibria and invariant manifolds joined by simple optimized maneuvers. Our main goal is to compute an approximate globally optimal solution which can serve as a good initial guess for iterative nonlinear control optimization. The described approach is exemplified by the optimal control of the spherical pendulum. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)