In this paper, we present an approach for designing correct-by-design controllers for cyber-physical systems composed of multiple dynamically interconnected uncertain systems. We consider networked discrete-time uncertain nonlinear systems with additive stochastic noise and model parametric uncertainty. Such settings arise when multiple systems interact in an uncertain environment and only observational data is available. We address two limitations of existing approaches for formal synthesis of controllers for networks of uncertain systems satisfying complex temporal specifications. Firstly, whilst existing approaches rely on the stochasticity to be Gaussian, the heterogeneous nature of composed systems typically yields a more complex stochastic behavior. Secondly, exact models of the systems involved are generally not available or difficult to acquire. To address these challenges, we show how abstraction-based control synthesis for uncertain systems based on sub-probability couplings can be extended to networked systems. We design controllers based on parameter uncertainty sets identified from observational data and approximate possibly arbitrary noise distributions using Gaussian mixture models whilst quantifying the incurred stochastic coupling. Finally, we demonstrate the effectiveness of our approach on a nonlinear package delivery case study with a complex specification, and a platoon of cars.

翻译：本文提出了一种针对由多个动态互联不确定系统组成的网络化信息物理系统的正确性保证控制器设计方法。我们考虑具有加性随机噪声和模型参数不确定性的离散时间不确定非线性网络系统。这类场景常见于多个系统在不确定环境中交互且仅能获取观测数据的情况。现有面向满足复杂时序规范的不确定系统网络的形式化控制器综合方法存在两个局限性：其一，现有方法假设随机性服从高斯分布，而组合系统的异质性通常会产生更复杂的随机行为；其二，所涉系统的精确模型通常不可获得或难以获取。为应对这些挑战，我们展示了如何将基于子概率耦合的不确定系统抽象控制综合方法扩展至网络化系统。我们基于从观测数据中辨识的参数不确定集设计控制器，并利用高斯混合模型近似可能具有任意分布的噪声，同时量化由此产生的随机耦合效应。最后，通过在具有复杂规范的非线性包裹投递案例研究以及车辆编队场景中的实验验证了该方法的有效性。