We propose two perturbation-based extremum seeking control (ESC) schemes for general single input single output nonlinear dynamical systems, having structures similar to that of the classical ESC scheme. We propose novel adaptation laws for the excitation signal amplitudes in each scheme that drive the amplitudes to zero. The rates of decay for both the laws are governed by the gradient measures of the unknown reference-to-output equilibrium map We show that the proposed ESC schemes achieve practical asymptotic convergence to the extremum with a proper tuning of the parameters in the proposed schemes. As the extremum is reached, and the magnitudes of the gradient measures become small, the excitation signal amplitudes converge to zero. Thus, the proposed schemes ensure that the excitation signal is driven to zero as the system output converges to a neighborhood of the extremum and the steady-state oscillations about the extremum, typically observed for the classical ESC schemes, are attenuated. Simulation examples are included to illustrate the effectiveness of the proposed schemes.

我们为一般的单输入单输出非线性动力系统提出了两种基于摄动的极值搜寻控制（ESC）方案，其结构与经典ESC方案的结构相似。在每种方案中，我们为激励信号幅度提出了新颖的自适应定律，以将幅度驱动为零。这两个定律的衰减率均由未知参考输出平衡图的梯度测度控制。我们表明，所提出的ESC方案通过对所提出方案中的参数进行适当调整，实现了极值的实际渐近收敛。随着达到极值，并且梯度度量的大小变小，激励信号幅度收敛到零。从而，提出的方案可确保当系统输出收敛到极值附近时，激励信号被驱动为零，并且衰减在典型ESC方案中通常观察到的极值附近的稳态振荡。包括仿真示例，以说明所提出方案的有效性。