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Providing a Basin of Attraction to a Target Region by Computation of Lyapunov-like Functions

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She,  Zhikun
Programming Logics, MPI for Informatics, Max Planck Society;

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Ratschan,  Stefan
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

She, Z., & Ratschan, S. (2006). Providing a Basin of Attraction to a Target Region by Computation of Lyapunov-like Functions. In 4th IEEE International Conference on Computational Cybernetics (pp. 245-249). MA, USA: IEEE.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-23C3-D
Abstract
In this paper, we present a method for computing a basin of attraction to a target region for non-linear ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly, and iteratively reduces the relaxation error by recursively decomposing the state space into hyper-rectangles. Tests on an implementation are promising.