Fast extremum seeking control without steady-state oscillation

An extremum seeking control (ESC) scheme based on switching between adaptive amplitude laws is presented in this paper to enhance both dynamic and steady-state performance. Two novel amplitude adaptation laws are developed using sliding-window dynamic gradient information, enabling more accurate prediction of output trends and ensuring that the excitation amplitude decays to zero upon crossing local extrema to reach the global maximum, thereby eliminating steady-state oscillations. To greatly improve dynamic performance without sacrificing steady-state accuracy, a Lyapunov-based switching strategy is employed to transition between the adaptive laws, allowing the system output to converge rapidly to the global maximum without oscillations. A rigorous stability proof is provided, and numerical simulations are conducted to demonstrate the effectiveness of the proposed scheme. The method is also applied to an anti-lock braking system (ABS) to verify its practical applicability.