This paper studies the control of safety-critical dynamical systems in the presence of adversarial disturbances. We seek to synthesize state-feedback controllers to minimize a cost incurred due to the disturbance, while respecting a safety constraint. The safety constraint is given by a bound on an H-inf norm, while the cost is specified as an upper bound on the H-2 norm of the system. We consider an online setting where costs at each time are revealed only after the controller at that time is chosen. We propose an iterative approach to the synthesis of the controller by solving a modified discrete-time Riccati equation. Solutions of this equation enforce the safety constraint. We compare the cost of this controller with that of the optimal controller when one has complete knowledge of disturbances and costs in hindsight. We show that the regret function, which is defined as the difference between these costs, varies logarithmically with the time horizon. We validate our approach on a process control setup that is subject to two kinds of adversarial attacks.

中文翻译：

---

具有对抗干扰的安全关键在线控制

本文研究了在存在对抗性干扰的情况下对安全关键动力系统的控制。我们寻求综合状态反馈控制器，以最大限度地减少由于干扰而产生的成本，同时尊重安全约束。安全约束由 H-inf 范数的边界给出，而成本则指定为系统 H-2 范数的上限。我们考虑一个在线设置，其中只有在选择了当时的控制器后才会显示每次的成本。我们提出了一种通过求解改进的离散时间 Riccati 方程来合成控制器的迭代方法。该方程的解强制执行安全约束。当一个人事后完全了解干扰和成本时，我们将这个控制器的成本与最优控制器的成本进行比较。我们表明，后悔函数（定义为这些成本之间的差异）随时间范围呈对数变化。我们在受到两种对抗性攻击的过程控制设置上验证了我们的方法。