Nonlinear Modeling by Interpolation Between Linear Dynamics and Its Application in Control

[+] Author and Article Information
Kiriakos Kiriakidis

Department of Weapons and Systems Engineering, United States Naval Academy, 105 Maryland Avenue, Annapolis, MD 21402kiriakid@usna.edu

J. Dyn. Sys., Meas., Control 129(6), 813-824 (Jan 25, 2007) (12 pages) doi:10.1115/1.2789473 History: Received December 21, 2005; Revised January 25, 2007

This paper proposes a finite series expansion to approximate general nonlinear dynamics models to arbitrary accuracy. The method produces an approximation of nonlinear dynamics in the form of an aggregate of linear models, weighted by unimodal basis functions, and results in a linear growth bound on the approximation error. Furthermore, this paper demonstrates that the proposed approximation satisfies the modeling assumptions for analysis based on linear matrix inequalities and hence widens the applicability of these techniques to the area of nonlinear control.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Basis functions α1, α2, and α3 for s=π∕4, π∕6, π∕12, and π∕36 (clockwise from top left)

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Figure 2

VDP: approximate (dashed) versus exact trajectories (solid) for s=59

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Figure 3

VDP: approximate (dashed) versus exact trajectories (solid) for s=515

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Figure 4

IPC: uniform (left) versus nonuniform spacing (right); approximate (dashed) versus exact trajectories (solid)

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Figure 5

IPC: stabilized trajectories in X=[−π∕4,π∕4]×[−π,π]; grid of 9×17 operating points



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