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Ensemble Control

State Assignment of Harmonic Oscillators:

A single control input is used to steer the state distribution of harmonic oscillators with natural frequencies between -10 and 10 from a star shape to a maple leaf. The state space is position on the horizontal axis and velocity on the vertical axis.

The control used in the previous example is given below.

Star to Maple control

The same problem is solved below for initial and final state dispersions in the form of a circle and a square.

The control used in the previous example is given below.

Circle to Square Control

The same problem is solved below for initial and final state dispersions in the form of the words “Green” and “Hall”.

The control used in the previous example is given below.

Green to Hall Control