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Extremum seeking (ES) addresses the control problems concerned with a nonlinear plant or objective function, aiming at finding and maintaining an unknown optimal operating condition that either maximizes or minimizes the nonlinearity. The transient behavior of an ES system being regulated away from its optimal operating condition is referred to as transient misdirection. This phenomenon not only results in the depression of control efficiency but is also undesirable in many practical applications. This article focuses on transient misdirection in a basic ES scheme and proposes a novel modification on the high-pass filter (HPF). The core methodology is to introduce an adaptive HPF with a time-varying cut-off frequency that is high during transients and low during steady states. The adaptive HPF-based ES scheme is applied to both static and Hammerstein plants, and a semi-global stability result of the obtained system is presented by performing a Lyapunov analysis. The proposed approach can considerably reduce transient misdirection without sacrificing the convergence rate, as illustrated through simulation examples, demonstrating its effectiveness, practical prospect, and advantage over nonadaptive approaches.
Li et al. (Fri,) studied this question.