Stability certification and identification of the stabilizable operating region of a system are two important concerns to ensure its operational safety/security and robustness. With the advent of machine-learning tools, these issues are specially important for systems with machine-learned components in the feedback loop. Here we develop a theory for stability and stabilizability of a class of neural-network controlled nonlinear systems, where the equilibria can drift when parametric changes occur. A Lyapunov based convex stability certificate is developed and is further used to devise an estimate for a local Lipschitz upper bound for a neural-network (NN) controller and a corresponding operating domain on the state space, containing an initialization set from where the closed-loop (CL) local asymptotic stability of each system in the class is guaranteed under the same controller, while the system trajectories remain confined to the operating domain. For computing such a robust stabilizing NN controller, a stability guaranteed training (SGT) algorithm is also proposed. The effectiveness of the proposed framework is demonstrated using illustrative examples.

翻译：稳定认证和确定一个系统可稳定运行的区域,是确保其运行安全/安保和稳健性的两个重要问题。随着机器学习工具的出现,这些问题对于在反馈环中具有机器学习组件的系统特别重要。我们在这里为一类神经网络控制的非线性系统的稳定性和可稳定性开发了理论,该类系统在参数变化发生时可以漂移。基于Lyapunov的 convex稳定性证书正在开发,并被进一步用于设计一个当地Lipschitz的估计数,用于神经网络控制器和州空间相应操作域的上限,其中包含一个初始化装置,即该类中每个系统的闭环(CL)局部无损稳定性在同一个控制器下得到保障,而系统轨迹仍局限于操作领域。对于计算这样一个稳健的NNC控制器,还提出了稳定性保障培训算法。拟议框架的有效性以示例的形式加以说明。