Asymptotic vs Projective Representation for Solutions of Dynamical System Equations

M. Cotsaftis (France)


Dynamical System, Power Flow, Asymptotic Representation of Solution


The problem of dynamical evolution of a system exhibiting internal branchings toward bifurcated states is reconsidered by observing that as a consequence the number of ”relevant” state space dimensions where power flows is varying with time. Classical projection method to represent the solution does no longer apply, and more adapted asymptotic method taking advantage of branched states characteristic time and space scales is discussed. Analytic expressions of the solution are given, allowing to construct the modified state space dynamics due to these branchings and to design a correct controller which selfconsistently accounts for the internal power flows created by the opening of in ternal branched modes. Application is made to com pliant actuated deformable one-link system.

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