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Controlling physical systems with symmetries

Grigoriev, R. O. and Cross, M. C. (1998) Controlling physical systems with symmetries. Physical Review E, 57 (2). pp. 1550-1554. ISSN 1063-651X. http://resolver.caltech.edu/CaltechAUTHORS:GRIpre98

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Abstract

Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular the selection of control parameters and their minimal number are determined by the irreducible representations of the symmetry group of the linearization about the orbit to be controlled. We use the general results to demonstrate the effect of symmetry on the control of two sample physical systems: a coupled map lattice and a particle in a symmetric potential.


Item Type:Article
Additional Information:©1998 The American Physical Society Received 22 July 1997 R.O.G is grateful to J. C. Doyle and R. Murray for valuable discussions. This work was partially supported by the NSF through Grant No. DMR-9013984.
Record Number:CaltechAUTHORS:GRIpre98
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:GRIpre98
Alternative URL:http://dx.doi.org/10.1103/PhysRevE.57.1550
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3134
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:16 May 2006
Last Modified:26 Dec 2012 08:52

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