This article proposes a novel adaptive robust control approach based on Gaussian processes (GPs) for the high-precision tracking problem of uncertain Euler–Lagrange (EL) systems with time-varying external disturbances. Given a prior dynamic model, the GP regression (GPR) technique is employed to obtain a nonparametric data-based uncertainty model, including its probabilistic confidence intervals. Based on the adaptive sliding mode control (ASMC) framework, the posterior means of GPs are utilized for dynamic compensation, whereas the posterior variances are applied to adjust the feedback gains. This proposed control strategy is robust against significant system uncertainty with low feedback gains. A novel adaptive law for updating hyperparameters based on tracking error feedback is presented, thereby improving the performance of both tracking control and GP modeling simultaneously. Compared to existing likelihood-based optimization methods, this hyperparameter adaptive law enables data-efficient and fast uncertainty learning for control applications. The proposed control strategy guarantees the semiglobal asymptotic convergence to zero tracking error with a specified probability. Simulations using an underwater robot model demonstrate that the utilization of GPs and hyperparameter adaptive law significantly improves the performance of tracking control and uncertainty learning.

中文翻译：

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使用高斯过程的不确定欧拉格朗日系统的自适应鲁棒控制


本文提出了一种基于高斯过程（GP）的新型自适应鲁棒控制方法，用于解决具有时变外部扰动的不确定欧拉-拉格朗日（EL）系统的高精度跟踪问题。给定先前的动态模型，采用 GP 回归 (GPR) 技术来获得基于非参数数据的不确定性模型，包括其概率置信区间。基于自适应滑模控制（ASMC）框架，利用GP的后验均值进行动态补偿，而后验方差则用于调整反馈增益。该控制策略对于低反馈增益的显着系统不确定性具有鲁棒性。提出了一种基于跟踪误差反馈更新超参数的新型自适应律，从而同时提高跟踪控制和GP建模的性能。与现有的基于似然的优化方法相比，这种超参数自适应律能够为控制应用提供数据高效且快速的不确定性学习。所提出的控制策略保证半全局渐近收敛于指定概率的零跟踪误差。使用水下机器人模型的仿真表明，GP 和超参数自适应律的使用显着提高了跟踪控制和不确定性学习的性能。