Comparative performances of synchronisation between different classes of chaotic systems using three control techniques

This paper puts forward the comparative performances for synchronisation between (i) systems from different chaotic system families, (ii) systems from the Unified Chaotic System (UCS) family, (iii) a hyperchaotic and a chaotic systems and (iv) identical chaotic systems. Three different well-known control techniques, i.e. Nonlinear Active Control (NAC), Sliding Mode Control (SMC) and Adaptive Control (AC) are used for synchronisation between various pairs of chaotic and/or hyperchaotic systems. Performances of NAC, SMC and AC techniques are investigated and compared with synchronisation of different pairs of chaotic systems based on the error dynamics and required control inputs. The integral square error and required control energy measures are considered for comparison. Finally, a generalised view on the use of the control techniques for synchronisation is finally proposed. Moreover, a new chaotic system is proposed and its qualitative analysis is done to illustrate the chaotic behaviour of the system. The new system is used as an example of synchronisation. MATLAB simulation results are presented which reflect the successful achievement of the objectives.