We propose a distributed model predictive control scheme for linear time-invariant constrained systems that admit a separable structure. To exploit the merits of distributed computation algorithms, the terminal cost and invariant terminal set of the optimal control problem need to respect the coupling structure of the system. Existing methods to address this issue typically separate the synthesis of terminal controllers and costs from the one of terminal sets, and do not explicitly consider the effect of the current and predicted system states on this synthesis process. These limitations can adversely affect performance due to small or even empty terminal sets. Here, we present a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the same optimization problem. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the terminal cost and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several numerical examples.

中文翻译：

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具有自适应终端集的线性系统的分布式模型预测控制


我们提出了一种用于允许可分离结构的线性时不变约束系统的分布式模型预测控制方案。为了发挥分布式计算算法的优点，最优控制问题的终端成本和不变终端集需要考虑系统的耦合结构。解决这一问题的现有方法通常将终端控制器和成本的合成与终端集之一分开，并且没有明确考虑当前和预测的系统状态对该合成过程的影响。由于终端装置较小甚至是空的，这些限制可能会对性能产生不利影响。在这里，我们提出了一个统一的框架，将稳定终端控制器和不变终端集的综合封装到同一优化问题中。李亚普诺夫稳定性和不变性的条件以允许终端成本和不变终端集接纳所需的分布式结构的方式强加在综合问题中。我们通过几个数值例子说明了所提出方法的有效性。