Neural Lyapunov Control for Nonlinear Systems with Unstructured Uncertainties
- Resource Type
- Conference
- Authors
- Wei, Shiqing; Krishnamurthy, Prashanth; Khorrami, Farshad
- Source
- 2023 American Control Conference (ACC) American Control Conference (ACC), 2023. :1901-1906 May, 2023
- Subject
- Aerospace
Bioengineering
Power, Energy and Industry Applications
Robotics and Control Systems
Transportation
Uncertainty
System dynamics
Neural networks
Estimation
Control systems
Robustness
Trajectory
- Language
- ISSN
- 2378-5861
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 two examples, such as an inverted pendulum system and a cart-pole system.