Dynamic Nonlinear Gradient Observer Based Extremum Seeking Control for Optimum Braking

The application of extremum seeking control (ESC) algorithm to antilock braking systems (ABSs) is attractive for maximizing the longitudinal braking force. Most currently reported results suffer from the drawback of steady-state oscillations around the extremum or the need to have the gradient information. In this article, a new ESC algorithm is proposed for application to ABSs to overcome these two drawbacks. The proposed algorithm is based on a novel dynamic nonlinear gradient observer (DNGO) and a longitudinal braking force estimator. The performance and the ultimate boundedness of the proposed ESC, DNGO, and the force estimator are analyzed. The proposed method is validated by simulation for dry and wet road surfaces and compared with two established results. The method is further validated on an experimental setup in the laboratory for dry and oily surfaces.