State transition learning with limited data for safe control of switched nonlinear systems

Area of Science:

• Control Theory
• Nonlinear Systems
• Machine Learning

Background:

• Real-world systems exhibit switching dynamics, necessitating models like switched systems.
• Integrating safety constraints into control synthesis for switched systems is a significant challenge.
• Limited system data complicates control design for switched nonlinear systems.

Purpose of the Study:

• To develop a learning-based control strategy for switched nonlinear systems under arbitrary switching laws.
• To ensure system stability and uphold safety constraints with minimal data.
• To leverage switching characteristics for enhanced control performance.

Main Methods:

• Employed control barrier function (CBF) method and Lyapunov theory for safety and stability.
• Developed a neural control barrier function and a neural Lyapunov function.
• Utilized a state transition learning approach for control policy synthesis.
• Incorporated policy loss and forward state estimation for policy learning.

Main Results:

• Successfully synthesized a safe controller for switched nonlinear systems.
• Demonstrated the ability to maintain stability and safety constraints.
• Validated the effectiveness of the neural barrier and Lyapunov functions.
• Showcased robust performance under arbitrary switching laws with limited data.

Conclusions:

• The proposed learning-based control strategy effectively addresses safety and stability in switched nonlinear systems.
• Neural network approximations of control barrier and Lyapunov functions offer a viable solution for complex systems.
• The state transition learning approach facilitates the design of safe and stable control policies.