Adaptive observer based-robust synchronization of switched fractional Rikitake systems with input nonlinearity

This paper mainly focuses on the robust synchronization of switched fractional-order improved Rikitake two-disk dynamo system which is a more general topology of the original Rikitake system. In particular, we first explore and design a simplified model very close to a real geophysical process which is described by an orbiting point, primarily using concepts from dynamical system theory. Dynamical properties, including symmetry, dissipation, stability of equilibria, Lyapunov exponents, and bifurcation, are analyzed on the basis of theoretical analysis and numerical simulation. Secondly, some less stringent conditions for adaptive control are derived when the system is subjected to external disturbances, parametric uncertainties and nonlinear input. The convergence of the state space trajectories with the overall robust asymptotic stability of the closed-loop system is obtained using the Lyapunov theory. To highlight our contribution, an illustrative example is presented to show the effectiveness and applicability of the proposed synchronization scheme. This proposal derives a systematic procedure for the design and control of a wide range of electromechanical systems. The results obtained in this work have not yet been reported in the literature to the best of the authors' knowledge and thus deserve dissemination.