We propose Kernel Predictive Control (KPC), a learning-based predictive control strategy that enjoys deterministic guarantees of safety. Noise-corrupted samples of the unknown system dynamics are used to learn several models through the formalism of non-parametric kernel regression. By treating each prediction step individually, we dispense with the need of propagating sets through highly non-linear maps, a procedure that often involves multiple conservative approximation steps. Finite-sample error bounds are then used to enforce state-feasibility by employing an efficient robust formulation. We then present a relaxation strategy that exploits on-line data to weaken the optimization problem constraints while preserving safety. Two numerical examples are provided to illustrate the applicability of the proposed control method.

中文翻译：

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KPC：具有确定性保证的基于学习的模型预测控制

我们提出了内核预测控制（KPC），这是一种基于学习的预测控制策略，享有确定性的安全保证。未知系统动力学的受噪声破坏的样本用于通过非参数核回归的形式学来学习几种模型。通过单独处理每个预测步骤，我们无需通过高度非线性的映射传播集合，该过程通常涉及多个保守的近似步骤。然后，通过采用有效的鲁棒公式，使用有限样本误差范围来增强状态可行性。然后，我们提出一种放松策略，该策略利用在线数据来削弱优化问题的约束，同时又能保持安全性。提供两个数值示例来说明所提出的控制方法的适用性。