Extremum-seeking control (ESC) is a useful tool for the steady-state performance optimization of plants for which limited knowledge about its dynamical behavior and disturbance situation is known. The case when the steady-state plant responses correspond to equilibrium solutions received a lot of attention. However, in many industrial applications plant performance is characterized by time-varying steady-state behavior. In those cases, no static parameter-to-steady-state performance map can be defined. In this work, we propose an ESC method that employs a so-called dynamic cost function to cope with time-varying steady-state responses of general nonlinear systems. We prove semi-global practical asymptotic stability of the closed-loop ESC scheme in the presence of bounded and time-varying external disturbances. Moreover, the working principle is illustrated by means of the real-time performance optimal tuning of a nonlinear control strategy for a motion control application.

极值搜索控制（ESC）是用于工厂稳态性能优化的有用工具，对于该设备的动态行为和扰动情况知之甚少。稳态工厂响应对应于平衡解的情况引起了很多关注。但是，在许多工业应用中，工厂性能的特征是时变稳态行为。在那些情况下，无法定义静态的参数到稳态性能图。在这项工作中，我们提出了一种ESC方法，该方法采用了所谓的动态成本函数来应对一般非线性系统的时变稳态响应。我们证明了在有界和时变外部干扰的存在下，闭环ESC方案的半全局实用渐近稳定性。此外，