Combination and Tracking Control of Chaotic Systems
Combination-control of two or more systems which may have important application in Josephson junction ratchet array, and other physical systems has not been explored. Most of the theoretical framework is on combination synchronization, and the need for combination- tracking control. In this paper tracking control of 2-D Duffing oscillator, 3-D Lorenz-Stenflo, 4-D Lorenz-Stenflo systems, as well as combination-tracking control of two, three, four and five systems evolving from different initial conditions were investigated. The scheme was investigated using different sets of five 2-D Duffing oscillator, 3-D Lorenz-Stenflo system and 4-D Lorenz-Stenflo systems evolving from different initial conditions. The control scheme was also investigated using the recursive backstepping control for the design of effective controllers, followed by numerical simulations using MATLAB. The results obtained from the time series graphs showed that, the control time is independent of the number of combined systems, combination behaviour is independent of the dimension of the combined systems, and that the chaotic attractor increases in size as the number of system increases. For a combination of n systems, the attractor’s sizes increase n-fold.