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Memristive Murali–Lakshmanan–Chua circuit; state-space representations; canonical forms; Luenberger observer; feedback control; gain vectors and matrices; pole placement.

In this paper we report the control and synchronisation of chaos in a memristive Murali–Lakshmanan–Chua (MLC) circuit. This circuit, introduced by the present authors in 2013, is basically a non-smooth system having two discontinuity boundaries by virtue of it having a flux-controlled active memristor as its nonlinear element. While the control of chaos has been effected using state feedback techniques, the concept of adaptive synchronisation and observer-based approaches have been used to effect synchronisation of chaos. Both these techniques are based on state space representation theory which is well known in the field of control engineering. As in our earlier works on this circuit, we have derived the Poincaré discontinuity mapping (PDM) and zero time discontinuity mapping (ZDM) corrections, both of which are essential for realising the true dynamics of non-smooth systems. Further, we have constructed the observer- and controller-based canonical forms of the state space representations, have set up the Luenberger observer, derived the controller gain vector to implement state feedback control and calculated the gain matrices for switch feed back and finally performed parameter estimation for effecting observer-based adaptive synchronisation. Our results obtained by numerical simulation include time plots, phase portraits, estimation of the parameters and convergence of error graphs and phase plots showing complete synchronisation.

A ISHAQ AHAMED¹ M LAKSHMANAN²

1. Department of Physics, Jamal Mohamed College (Affiliated to Bharathidasan University), Tiruchirappalli 620 020, India
2. Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India

Published

17 October 2020

Manuscript received

24 January 2020

Manuscript revised

25 June 2020

Accepted

29 July 2020

Final version published online

17 October 2020