Stabilization of a chaotic oscillator via a class of integral controllers under input saturation

This work presents the straightforward design of an integral controller with an anti-windup structure to prevent undesirable behavior when actuator saturation is considered, and the proposed controller improves the performance of the closed-loop dynamics of a class of nonlinear oscillators. The proposed integral controller has an adaptive control gain, which includes the absolute value of the named control error to turn off the integral action when it is saturated. Closed-loop stability analysis is performed under the Lyapunov theory framework, where it can be concluded that the system behaves in an asymptotically stable way. The proposed methodology is successfully applied to a Rikitake-type oscillator, considering a single input-single output (SISO) structure for regulation and tracking trajectory purposes. For comparison, an equivalent fixed gain integral controller is also implemented to analyze the corresponding anti-windup properties of the proposed control structure. Numerical experiments are conducted, showing the superior performance of the proposed controller.