S. Kaart et al., Synchronizing chaos in an experimental chaotic pendulum using methods fromlinear control theory, PHYS REV E, 59(5), 1999, pp. 5303-5312
Linear feedback control, specifically model predictive control (MPC), was u
sed successfully to synchronize an experimental chaotic pendulum both on un
stable periodic and aperiodic orbits. MPC enables tuning of the controller
to give an optimal controller performance. That is, both the fluctuations a
round the target trajectory and the necessary control actions are minimized
using a least-squares solution of the linearized problem. It is thus shown
that linear control methods can be applied to experimental chaotic systems
, as long as an adequate model is available that can be linearized along th
e desired trajectory. This model is used as an observer, i.e., it is synchr
onized with the experimental pendulum to estimate the state of the experime
ntal pendulum. In contrast with other chaos control procedures like the map
-based Ott, Grebogi, and York method [Phys. Rev. Lett. 64, 1196 (1990)], th
e continuous type feedback control proposed by Pyragas [Phys. Lett. A 170,
421 (1992)], or the feedback control method recently proposed by Brown and
Rulkov [Chaos 7 (3), 395 (1997)], the procedure outlined in this paper auto
matically results in a choice for the feedback gains that gives optimum per
formance, i.e., minimum fluctuations around the desired trajectory using mi
nimum control actions. [S1063-651X(99)09505-7].