The Implicit Function Theorem with Applications in Dynamics and Control
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abstract
The implicit function theorem is a statement of the existence, continuity, and differentiability of a function or set of functions. The theorem is closely related to the convergence of Newton's method for nonlinear equations, the existence and uniqueness of solutions to nonlinear differential equations, and the sensitivity of solutions to these nonlinear problems. The implicit function theorem is presented, and high order sensitivity equations are generated using implicit differentiation. Once a nominal solution is known, these sensitivities are used to construct a family of neighboring solutions. Based on results presented in the paper, the implicit function approach shows great promise compared with current methods in generating families of neighboring solutions to problems in dynamics and control. Copyright 2010 by Matthew Harris.
name of conference
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
