Disturbance Rejection Extremum Seeking: A Sliding Mode Control Approach

This letter investigates the sliding mode extremum seeking control problem for nonlinear systems with disturbances to improve the disturbance rejection capability, delivering promising searching accuracy and efficiency under disturbances. The existing results in sliding mode extremum seeking control suffer from the drawback of unsatisfactory transient performance and slow convergence speed when disturbances, especially unmatched disturbances, are injected into the system. To this end, a disturbance rejection sliding mode extremum seeking control approach is proposed in this letter. A nonlinear disturbance observer is developed for disturbance estimation, and then a disturbance rejection sliding mode extremum seeking control algorithm is proposed by exploiting the disturbance estimation. Under the proposed approach, the disturbances can be online estimated and compensated. As a result, the cost function is less disturbed by unknown disturbances, and faster convergence speed as well as shorter recovery time can be obtained. The proposed method is applied for directional antenna automatic tracking system. Simulation results show that the newly proposed searching control approach outperforms the baseline extremum searching approaches in terms of much more reliable and high efficiency searching performance under disturbances.