In this work, we establish different control design approaches for discrete-time systems, which build upon the notion of finite-step control Lyapunov functions (fs-CLFs). The design approaches are formulated as optimization problems and solved in a model predictive control (MPC) fashion. In particular, we establish contractive multi-step MPC with and without reoptimization and compare it to classic MPC. The idea behind these approaches is to use the fs-CLF as running cost. These new design approaches are particularly relevant in situations where information exchange between plant and controller cannot be ensured at all time instants. An example shows the different behavior of the proposed controller design approaches.

中文翻译：

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通过有限步控制 Lyapunov 函数控制离散时间非线性系统

在这项工作中，我们为离散时间系统建立了不同的控制设计方法，这些方法建立在有限步控制李雅普诺夫函数 (fs-CLFs) 的概念之上。设计方法被表述为优化问题，并以模型预测控制 (MPC) 方式解决。特别是，我们建立了带有和不带有重新优化的收缩多步 MPC，并将其与经典 MPC 进行了比较。这些方法背后的想法是使用 fs-CLF 作为运行成本。这些新的设计方法在无法始终确保工厂和控制器之间的信息交换的情况下尤其重要。一个例子显示了所提出的控制器设计方法的不同行为。