A new chaotic systems with hidden attractors for dynamical analysis, control and its engineering applications - Aceng Sambas
Chaotic systems with hidden attractors constitute a new branch of study in the chaos literature. The problem of numerical localization, computation, and analytical investigation of hidden attractors is much more challenging. This happens, since in this case there is no possibility to use information about equilibria for organization of similar transient processes in the standard computational procedure. To address the problem, a dynamical method and Multistability analysis are proposed. A detailed study of the new chaotic systems has been carried out by analyzing the Lyapunov exponent spectrum, bifurcation diagram, Poincare map, offset boosting and multi stability . Furthermore, the dynamic equations of the new chaotic systems are implemented with an electronic circuit and simulations via MultiSim. The complete synchronisations of the new chaotic systems have been achieved via various control methods. The control methods considered for this study are adaptive control, backstepping control, sliding mode control and passive control. In engineering applications, experiments are carried out on mobile robots models to test the effectiveness of mobile robot performance with a chaotic control system. Three new chaotic systems have been obtained with no equilibrium point, three new chaotic systems have been obtained with line equilibrium points and six new chaotic systems have been obtained with closed curve equilibrium points. The mathematical chaotic models and parameter values are obtained after rigorous simulations to find suitable parameter values for the occurrence of chaotic behavior. As a control application, a pair of new chaotic systems, called master-slave systems, has been completely synchronized with asymptotic matching of the trajectories of the systems. Furthermore, MultiSim circuit outputs of the new chaotic systems have been obtained showing good matching with the MATLAB simulations. This is indicated by a good similarity of the plots of the chaotic attractors obtained with MATLAB and MultiSim simulations. In wireless mobile robot, the trajectory obtained using the new chaotic system shows a 67 % percentage of the work area passed by mobile robot. The dynamic analysis shows the new chaotic systems with hidden attractors have complex properties. The MultiSim simulation outputs show a good matching with the new chaotic systems with hidden attractors. The control results show that the sliding mode control method gives the best performance for the synchronization of chaotic systems. This is indicated by fast error convergence for the sliding mode control based synchronization of the new chaotic systems. Based on the large coverage of area passed by the mobile robot, the proposed chaotic system is very good for the control system in mobile robot navigation compared with in other performance result in the literature.