Construction of Control Lyapunov Function with Region of Attraction Using Union Theorem in Sum-Of-Squares Optimization

Control Lyapunov function (CLF) paves the way for designing a certified controller with a known stable region, which is the out-most importance in control systems. Sum-of-Squares (SOS) optimization is one method to construct the CLF with this stable region known as a region of attraction (ROA). However, existing methods yield quite conservative results. A new approach for constructing CLF overcoming existing limitations is proposed in this paper. The proposed method is based on the Union Theorem in sum-of-squares optimization, which enables the application of more than one variable size region generated by positive functions known as the Shape Function. Numerical simulations demonstrate the effectiveness of the proposed method, which outperforms the existing methods and provides a significantly enhanced ROA.

Automated summary

Control Lyapunov function (CLF) is crucial for designing a certified controller with a known stable region in control systems. Existing methods for constructing the CLF with a stable region known as region of attraction (ROA) often yield conservative results. This paper proposes a new approach based on the Union Theorem in sum-of-squares optimization, which utilizes multiple variable size regions generated by positive functions called Shape Functions. Numerical simulations demonstrate the effectiveness of the proposed method, which outperforms existing methods and provides a significantly enhanced ROA.