This article addresses the problem of extremum seeking of a continuous-time dynamical system with a single input and a single output. A Super-Twisting-based optimization algorithm is proposed to compute the input that leads to the extremum value of an unknown convex objective function. Our optimization algorithm requires the input–output gradient of the system’s response at steady state, which we compute throughout a Super-Twisting-based differentiator. Feasibility of the proposed extremum seeking strategy is demonstrated by two simulation examples. The first one is an example of interest in academy. The second one is a novel biohydrogen production process.

中文翻译：

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基于Super-Twisting算法的极值搜索控制和梯度估计

本文解决了具有单输入和单输出的连续时间动态系统的极值搜索问题。提出了一种基于超级扭曲的优化算法来计算导致未知凸目标函数极值的输入。我们的优化算法需要稳定状态下系统响应的输入-输出梯度，我们通过基于 Super-Twisting 的微分器计算该梯度。所提出的极值搜索策略的可行性通过两个仿真示例得到了证明。第一个是对学院感兴趣的例子。第二个是一种新的生物制氢工艺。