This article aims at the safety-critical control synthesis of network systems such that the satisfaction of the safety constraints can be guaranteed. To handle the large state dimension of such systems, an assume-guarantee contract is used to break the large synthesis problem into smaller subproblems. Parameterized signal temporal logic (pSTL) is used to formally describe the behaviors of the subsystems which we use as the template for the contract. We show that robust control invariant sets (RCIs) for the subsystems can be composed to form a robust control invariant set (RCI) for the whole network system under a valid assume-guarantee contract. An epigraph algorithm is proposed to solve for a contract that is valid, an approach that has linear complexity for sparse networks, which leads to a RCI for the whole network system. Implemented with control barrier function (CBF), the state of each subsystem is guaranteed to stay within the safe set. Furthermore, we propose a contingency tube model predictive control approach based on the RCI, which is capable of handling severe contingencies, including topology changes of the network. A power grid example is used to demonstrate the proposed method. The simulation result includes both set point control and contingency recovery, and the safety constraint is always satisfied.

中文翻译：

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具有控制屏障功能和假定担保合同的网络系统的安全关键控制综合

本文旨在实现网络系统的安全关键控制综合，以确保满足安全约束条件。为了处理此类系统的大型状态维度，可以使用假设担保合同将大型综合问题分解为较小的子问题。参数化的信号时间逻辑（pSTL）用于形式化描述子系统的行为，我们将其用作合同的模板。我们显示了子系统的鲁棒控制不变集（RCI）可以组成一个有效的假定保证合同下整个网络系统的鲁棒控制不变集（RCI）。提出了一种题词算法来求解有效合同，该方法对于稀疏网络具有线性复杂度，从而导致整个网络系统的RCI。通过控制屏障功能（CBF）实施，可以确保每个子系统的状态都保持在安全范围内。此外，我们提出了一种基于RCI的应急管模型预测控制方法，该方法能够处理严重的突发事件，包括网络的拓扑变化。以电网为例来说明所提出的方法。仿真结果包括设定点控制和应变恢复，并且始终满足安全约束。