ISSN:
1531-5878
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract Given a nonlinear control system $$\dot x(t) = f(x(t)) + \sum\limits_{i = 1}^m {u_i (t)g_i (x(t))}$$ on ℝ n and a pointx 0 in ℝ n , we want to approximate the system nearx 0 by a linear system. Of course, one approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that we should construct a linear approximation based on Lie bracket matching atx 0. In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, we show that there is a coordinate system for ℝ n nearx 0 in which these two types of linearizations agree. We indicate the importance of this agreement by examining the time responses of the nonlinear system and its linear approximation and comparing the lower-order kernels in Volterra expansions of each.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01599618
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