We take a divide and conquer approach to design controllers for reachability problems given large-scale linear systems with polyhedral constraints on states, controls, and disturbances. Such systems are made of small subsystems with coupled dynamics. We treat the couplings as additional disturbances and use assume-guarantee (AG) contracts to characterize these disturbance sets. For each subsystem, we design and implement a robust controller locally, subject to its own constraints and contracts. The main contribution of this paper is a method to derive the contracts via a novel parameterization and a corresponding potential function that characterizes the distance to the correct composition of controllers and contracts, where all contracts are held. We show that the potential function is convex in the contract parameters. This enables the subsystems to negotiate the contracts with the gradient information from the dual of their local synthesis optimization problems in a distributed way, facilitating compositional control synthesis that scales to large systems. We present numerical examples, including a scalability study on a system with tens of thousands of dimensions, and a simple case study on applying our method to a distributed Model Predictive Control (MPC) problem in a power system.

中文翻译：

---

通过假设保证合同的凸优化线性系统的组合综合


考虑到对状态、控制和扰动具有多面体约束的大规模线性系统，我们采用分而治之的方法来设计控制器，以解决可达性问题。此类系统由具有耦合动力学的小型子系统组成。我们将耦合视为附加扰动，并使用假设保证（AG）契约来表征这些扰动集。对于每个子系统，我们在本地设计并实现一个强大的控制器，并遵守其自身的约束和合同。本文的主要贡献是一种通过新颖的参数化和相应的势函数来推导合约的方法，该势函数描述了控制器和合约的正确组合的距离，其中所有合约都被持有。我们证明了合约参数中的势函数是凸的。这使得子系统能够以分布式方式利用来自其本地综合优化问题的对偶的梯度信息来协商合同，从而促进可扩展到大型系统的组合控制综合。我们提供了数值示例，包括对数万维系统的可扩展性研究，以及将我们的方法应用于电力系统中的分布式模型预测控制（MPC）问题的简单案例研究。