Controlling Physical Systems with Symmetries

Details Controlling Physical Systems with Symmetries Controlling Physical Systems with Symmetries

1997-07-21

arxiv.org/abs/chao-dyn/9707020v1

Nonlinear Sciences

Chaotic Dynamics

6 pages

Scientific paper

10.1103/PhysRevE.57.1550

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.

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