Periodic switching function based sliding mode control applied to output-feedback extremum-seeking problem

In a companion paper submitted to VSS 2010, we have addressed the design of sliding mode tracking control for single-input-single-output (SISO) uncertain nonlinear plants with unknown sign of the high frequency gain, that is, with unknown control direction. We have demonstrated that it is possible to achieve global exact tracking using only output-feedback by combining a periodic switching function with a norm state observer framework. One significant advantage of this scheme was its robustness to time-varying control direction. In the present paper, we show that this property makes it adequate for solving extremum-seeking problems using only output-feedback for relative degree one strongly nonlinear systems. Applications to a nonderivative optimizer and to the wheel slip control in Antilock Braking Systems (ABS) illustrate the viability of the proposed control scheme.