We present an effective approach for controlling chaos by using a differential geometric method. It has been shown that the proposed method can control chaotic motion not only to a steady state but also to any desired periodic orbit. The main characteristic of the method is to algebraically transform a nonlinear dynamics into a linear one, so that linear control techniques can be applied. To demonstrate the feasibility of our proposed method, a Lorenz system under different designed requirements is illustrated.

• Received 18 August 1994

DOI:https://doi.org/10.1103/PhysRevLett.75.2952