2023/03/16 by S. Wei, Wei, Shiqing, P. Krishnamurthy +3
Engineering · #Adaptive Control of Nonlinear Systems #Control Systems and Identification #FOS: Electrical engineering #Fault Detection and Control Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2303.09678
openalex publication_date 2023/03/16 · openalex created_date 2023/03/21 · openalex updated_date 2026/07/28
Stabilizing controller design and region of attraction (RoA) estimation are essential in nonlinear control. Moreover, it is challenging to implement a control Lyapunov function (CLF) in practice when only partial knowledge of the system is available. We propose a learning framework that can synthesize state-feedback controllers and a CLF for control-affine nonlinear systems with unstructured uncertainties. Based on a regularity condition on these uncertainties, we model them as bounded disturbances and prove that a CLF for the nominal system (estimate of the true system) is an input-to-state stable control Lyapunov function (ISS-CLF) for the true system when the CLF's gradient is bounded. We integrate the robust Lyapunov analysis with the learning of both the control law and CLF. We demonstrate the effectiveness of our learning framework on several examples, such as an inverted pendulum system, a strict-feedback system, and a cart-pole system.