Abstract We develop a method for computing controlled invariant sets of discrete-time affine systems using Sum-of-Squares programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets but our work also improves the state of the art for the particular case of LTI systems. The task is reduced to a semidefinite programming problem by enforcing an invariance relation in the dual space of the geometric problem. The paper ends with an application to safety critical model predictive control.

中文翻译：

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控制不变集的平方和方法在模型预测控制中的应用

摘要 我们开发了一种使用平方和编程计算离散时间仿射系统的受控不变集的方法。我们将我们的方法应用于控制器设计问题，以使用多面体安全集切换仿射系统，但我们的工作还改进了 LTI 系统特定情况的最新技术。通过在几何问题的对偶空间中强制执行不变关系，该任务被简化为半定规划问题。本文以对安全关键模型预测控制的应用结束。