| Summary: | 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.
|
|---|