Control of Switched Electrical Networks
Using Averaging on Lie Groups

N.E. Leonard and P.S. Krishnaprasad

In Proceedings of the 33rd IEEE Conference on Decision and Control, 1994, p.1919-1924.


In this paper we apply the theory of averaging and motion control on Lie groups \cite{NEEL_thesis} to the problem of controlling energy transfers between dynamic storage elements in switched electrical networks. The switched networks of interest have bilinear state-space models in which the control $u$, representing the position of the switch, takes value in the set $\{0,1\}$. The corresponding state transition matrix can be described by a right-invariant system evolving on a matrix Lie group \cite{Wood}, and as such we can use our theory to derive high-order average approximations to the evolution of the state transition matrix. We show how to use these average solutions to control energy transfers for a simple network that models the conversion portion of a dc-dc converter. Our approach provides an alternative to the feedback approach of Sira-Ramirez \cite{SiraRamirez87} which is based on variable structure systems with sliding regimes. Our methodology is based on open-loop control (combined with feedback if desired) and thus ensures that prescribed energy transfers can be accomplished with a finite number of switchings. This avoids chattering problems sometimes associated with sustaining sliding motions.

Postscript Version (6 pages postscript)

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