Synchronizing chaos in an experimental chaotic pendulum using methods fromlinear control theory

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].