A simple and efficient method for controlling high dimensional discrete-time chaotic systems is proposed in this paper. This method is implemented similar to the OGY method, and is feasible for practical experiments. The key component is to assign the eigenvalues of a linearized map by using the well-known pole placement technique. According to the Cayley-Hamilton theorem, the trajectory will converge to the desired fixed point after n iterations at most (n is the dimension of the map), if the real trajectory of the chaotic system falls within the neighborhood of the desired fixed point. The proposed approach improves the convergence rate and the robustness of the OGY method, especially for the case where the modulus of the stable eigenvalue is close to unity. The simulations illustrate the performance of our presented controller for controlling a chaotic system compared to the OGY method.
Tsai, Hsun-Heng; Fuh, Chyun-Chau; and Tung, Pi-Cheng
"Fast Convergence Control Approach for High Dimensional Chaotic Systems,"
Journal of Marine Science and Technology: Vol. 10:
2, Article 1.
Available at: https://jmstt.ntou.edu.tw/journal/vol10/iss2/1