In the era of Industrial 4.0, the next-generation control system regards the cyber-physical system (CPS) as the core ingredient thanks to the comprehensive integration of physical systems, online computation, networking and control. A reliable, stable and resilient CPS should pledge robustness and safety. A significant concern in CPS development arises from security issues since the CPS is vulnerable to physical constraints, ubiquitous uncertainties and malicious cyber attacks. The integration of the stochastic model predictive control (MPC) framework and the resilient mechanism is a possible approach to guarantee robustness in the presence of stochastic uncertainties and enable resilience against cyber attacks. This review paper aims to offer a detailed overview of existing stochastic MPC algorithms and their CPS applications. More specifically, we first review existing stochastic MPC algorithms for both linear and nonlinear systems subject to probabilistic constraints. We then discuss how to extend the stochastic MPC framework to incorporate resilience mechanisms for constrained CPS under various malicious attacks. Finally, we present an architectural stochastic MPC-based framework for resilient CPS and identify future research challenges.

This article is part of the theme issue ‘Towards symbiotic autonomous systems’.

工业4.0时代，下一代控制系统以信息物理系统（CPS）为核心要素，实现了物理系统、在线计算、网络化和控制的全面集成。一个可靠、稳定和有弹性的 CPS 应该保证稳健性和安全性。CPS 开发中的一个重要问题来自安全问题，因为 CPS 容易受到物理约束、无处不在的不确定性和恶意网络攻击的影响。随机模型预测控制 (MPC) 框架和弹性机制的集成是一种可能的方法，可以在存在随机不确定性的情况下保证鲁棒性，并能够抵御网络攻击。本综述旨在详细概述现有的随机 MPC 算法及其 CPS 应用。进一步来说，我们首先回顾了受概率约束的线性和非线性系统的现有随机 MPC 算法。然后，我们讨论如何扩展随机 MPC 框架以在各种恶意攻击下为受限 CPS 合并弹性机制。最后，我们提出了一个基于架构随机 MPC 的弹性 CPS 框架，并确定了未来的研究挑战。

这篇文章是主题问题“走向共生自治系统”的一部分。