论文标题
通过快速可靠的基于神经网络的近似值对多重系统的稳定稳定
Robust stabilization of polytopic systems via fast and reliable neural network-based approximations
论文作者
论文摘要
我们考虑基于多物质不确定性的线性系统的传统稳定控制器的快速可靠神经网络（NN）的设计，包括具有可变结构的控制定律以及基于（最小）选择策略的控制定律。基于最新的具有保证结构属性的可靠控制替代物的方法，我们开发了一种系统的程序，以证明训练有素的基于培训的矫正线性单元（RELU）近似近似替代了这种传统控制器时，线性不确定系统的闭环稳定性和性能。首先，我们提供了足够的条件，这涉及基于RELU的和传统控制器的状态输入映射之间最坏的案例近似误差，从而确保该系统最终在以可调节大小和收敛速率的集合中界定。然后，我们开发了一种离线，混合优化的方法，该方法使我们能够准确地计算该数量。
We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a (minimal) selection policy. Building upon recent approaches for the design of reliable control surrogates with guaranteed structural properties, we develop a systematic procedure to certify the closed-loop stability and performance of a linear uncertain system when a trained rectified linear unit (ReLU)-based approximation replaces such traditional controllers. First, we provide a sufficient condition, which involves the worst-case approximation error between ReLU-based and traditional controller-based state-to-input mappings, ensuring that the system is ultimately bounded within a set with adjustable size and convergence rate. Then, we develop an offline, mixed-integer optimization-based method that allows us to compute that quantity exactly.
