This paper presents a novel approach to synthesize positive invariant sets for unmodeled nonlinear systems using direct data-driven techniques. The data-driven invariant sets are used to design a data-driven command governor that selects a command for the closed-loop system to enforce constraints. Using basis functions, we solve a semi-definite program to learn a sum-of-squares Lyapunov-like function whose unity level-set is a constraint admissible positive invariant set, which determines the constraint admissible states and input commands. Leveraging Lipschitz properties of the system, we prove that tightening the model-based design ensures robustness of the invariant set to the inherent plant uncertainty in a data-driven framework. To mitigate the curse-of-dimensionality, we repose the semi-definite program into a linear program. We validate our approach through two examples: First, we present an illustrative example where we can analytically compute the maximum positive invariant set and compare with the presented data-driven invariant set. Second, we present a practical autonomous driving scenario to demonstrate the utility of the presented method for nonlinear systems.

中文翻译：

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用于非线性系统的数据驱动不变量集，适用于命令调节器


本文提出了一种使用直接数据驱动技术为未建模非线性系统合成正不变集的新方法。数据驱动的不变量集用于设计数据驱动的命令调节器，该调节器为闭环系统选择一个命令来强制执行约束。使用基函数，我们求解一个半定程序来学习一个类似李雅普诺夫的平方和函数，其单位水平集是一个约束可接受的正不变量集，它决定了约束可接受的状态和输入命令。利用系统的 Lipschitz 属性，我们证明，收紧基于模型的设计可以确保不变量集对数据驱动框架中固有的工厂不确定性的稳健性。为了减轻维数的诅咒，我们将半定规划放入线性规划中。我们通过两个例子来验证我们的方法：首先，我们提供了一个说明性的例子，我们可以在其中分析计算最大正不变量集，并与所呈现的数据驱动的不变量集进行比较。其次，我们提出了一个实际的自动驾驶场景，以证明所提出的方法在非线性系统中的实用性。