Smooth extremum-seeking control via second order sliding mode

An extremum-seeking control scheme enforced by a second order sliding mode control strategy is proposed in this paper. It is characterized by the advantage of "second order" sliding mode design with smooth control input and derivative of sliding manifold. Chattering phenomena are greatly reduced. The stability conditions and performance criterions are given and proved for general plant modeled. Under these conditions, the objective plant will run within a small vicinity of the peak value of its performance index stably. The proposed extremum-seeking control strategy is practical for systems that do not tolerate high frequency alternating control signals and chattering arisen from delays.