论文标题
使用神经网络控制器的系统使用二次约束的稳定性分析
Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllers
论文作者
论文摘要
提出了一种方法来通过神经网络控制器分析反馈系统的稳定性。给出了两个稳定定理，以证明渐近稳定性并计算到吸引区域（ROA）的椭圆形内置。第一个定理解决了线性时间不变的系统，并将Lyapunov理论与局部（部门）二次约束结合在一起，以绑定神经网络中的非线性激活函数。第二个定理允许系统使用积分二次约束（IQC）捕获其输入/输出行为，包括未建模的动力学，斜率限制非线性和时间延迟等扰动。反过来，这允许逐一IQC通过捕获其斜率限制来完善激活功能的描述。两种结果都依赖于半决赛编程来近似ROA。该方法在具有训练的神经网络的系统上说明，以稳定非线性倒的摆和具有执行器不确定性的车辆横向动力学。
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction (ROA). The first theorem addresses linear time-invariant systems, and merges Lyapunov theory with local (sector) quadratic constraints to bound the nonlinear activation functions in the neural network. The second theorem allows the system to include perturbations such as unmodeled dynamics, slope-restricted nonlinearities, and time delay, using integral quadratic constraint (IQCs) to capture their input/output behavior. This in turn allows for off-by-one IQCs to refine the description of activation functions by capturing their slope restrictions. Both results rely on semidefinite programming to approximate the ROA. The method is illustrated on systems with neural networks trained to stabilize a nonlinear inverted pendulum as well as vehicle lateral dynamics with actuator uncertainty.
