Improved Fixed-Time Gradient-Based Multivariable Extremum Seeking Algorithm

Abstract

While the fixed-time gradient-based multivariable extremum seeking (FxTGMES) algorithm guarantees convergence within a bounded time independent of initial conditions, its nonlinear power terms often induce excessively large initial control gains. This inherently leads to pronounced transient overshoot and degrades the overall dynamic response. To address this issue, an improved fixed-time gradient-based multivariable extremum seeking (IFxTGMES) algorithm is proposed by integrating a dynamic compensation network. Specifically, a low-pass filter is employed to attenuate the high-gain-induced transient overshoot, while a proportional-derivative (PD) feedback loop is introduced to provide phase lead compensation, effectively neutralizing the inherent phase lag caused by the filter. Simulation results verify that the proposed IFxTGMES algorithm successfully suppresses the initial transient overshoot and enhances dynamic response quality, while strictly preserving the fixed-time convergence property.