Robust Stability of Neural-Network-Controlled Nonlinear Systems With Parametric Variability

Stability certification and identification of a safe stabilizing initial set are two important concerns in ensuring operational safety, stability, robustness dynamical systems. With the advent machine-learning tools, these issues need to be addressed for systems with machine-learned components feedback loop. To develop general theory stability stabilizability neural network (NN)-controlled nonlinear subject bounded parametric variations, Lyapunov-based certificate is proposed further used devise maximal Lipschitz bound class NN controllers, also corresponding Region Attraction (RoA) within user-specified safety set. compute robustly controller that maximizes system’s long-run utility, stability-guaranteed training (SGT) algorithm proposed. The effectiveness framework validated through an illustrative example.