Model predictive control allows to provide high performance and safety guarantees in the form of constraint satisfaction. These properties, however, can be satisfied only if the underlying model, used for prediction, of the controlled process is sufficiently accurate. One way to address this challenge is by data-driven and machine learning approaches, such as Gaussian processes, that allow to refine the model online during operation. We present a combination of an output feedback model predictive control scheme and a Gaussian process-based prediction model that is capable of efficient online learning. To this end, the concept of evolving Gaussian processes is combined with recursive posterior prediction updates. The presented approach guarantees recursive constraint satisfaction and input-to-state stability with respect to the model–plant mismatch. Simulation studies underline that the Gaussian process prediction model can be successfully and efficiently learned online. The resulting computational load is significantly reduced via the combination of the recursive update procedure and by limiting the number of training data points while maintaining good performance.

中文翻译：

---

具有高斯过程模型和稳定性保证的基于在线学习的模型预测控制

模型预测控制允许以约束满足的形式提供高性能和安全保证。然而，只有当用于预测的受控过程的基础模型足够准确时，才能满足这些属性。解决这一挑战的一种方法是通过数据驱动和机器学习方法，例如高斯过程，允许在操作期间在线改进模型。我们提出了输出反馈模型预测控制方案和能够高效在线学习的基于高斯过程的预测模型的组合。为此，将演化高斯过程的概念与递归后验预测更新相结合。所提出的方法保证了递归约束满足和输入到状态关于模型-设备失配的稳定性。仿真研究强调，高斯过程预测模型可以成功且高效地在线学习。通过结合递归更新程序和限制训练数据点的数量，同时保持良好的性能，由此产生的计算负载显着减少。