Adaptive Control of Chaotic Nonlinear Gyros with Uncertain Coefficients of Dynamical Model

In this paper, controlling the gyros with linear plus cubic damping is considered. Hence, an adaptive control algorithm is proposed to overcome the uncertainties in model parameters and the chaotic behavior of gyroscopes. It is noted that for general applications dynamic model coefficient of gyros is not precisely determined, on the other hand, with respect to a particular coefficient gyroscopes demonstrate chaotic responses. The designed controller guarantees the tracking property and closed loop stability, despite the model uncertainties. The proposed algorithm is then modified to meet the control objectives without estimating the model parameters simplifying the implementation procedure. The stability analysis is presented based on the Lyapunov stability theorem. In order to show the effectiveness of the method, several simulations are also performed. With respect to the result, it is concluded that the performance of adaptive mechanism is verified the convergence of tracking error to zero is conformed; and the closed-loop stability is also verified.