We present a Model Predictive Control (MPC) strategy for unknown input-affine nonlinear dynamical systems. A non-parametric method is used to estimate the nonlinear dynamics from observed data. The estimated nonlinear dynamics are then linearized over time varying regions of the state space to construct an Affine Time Varying (ATV) model. Error bounds arising from the estimation and linearization procedure are computed by using sampling techniques. The ATV model and the uncertainty sets are used to design a robust Model Predictive Control (MPC) problem which guarantees safety for the unknown system with high probability. A simple nonlinear example demonstrates the effectiveness of the approach where commonly used linearization methods fail.

中文翻译：

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用线性时变 MPC 控制未知非线性系统

我们提出了未知输入仿射非线性动力系统的模型预测控制 (MPC) 策略。非参数方法用于从观测数据估计非线性动力学。然后将估计的非线性动力学在状态空间的时变区域线性化，以构建仿射时变 (ATV) 模型。估计和线性化过程产生的误差界限是通过使用采样技术计算的。ATV 模型和不确定性集用于设计鲁棒模型预测控制 (MPC) 问题，以高概率保证未知系统的安全。一个简单的非线性示例证明了该方法在常用线性化方法失败的情况下的有效性。