Open AccessComputing an invariance kernel with target by computing Lyapunov‐like functions
Author(s) -
She Zhikun,
Xue Bai
Publication year - 2013
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2013.0275
Subject(s) - curse of dimensionality , reachability , lyapunov function , kernel (algebra) , dimension (graph theory) , dynamical systems theory , state space , mathematics , computer science , scalability , mathematical optimization , algorithm , nonlinear system , artificial intelligence , discrete mathematics , physics , quantum mechanics , pure mathematics , statistics , database
Reachability analysis and viability theory play an important role in control synthesis and trajectory analysis of constrained dynamical systems, many methods are known for computing them in low‐dimensional non‐linear systems, but these well‐known methods rely on gridding the state space and hence suffer from the curse of dimensionality. In this study, for systems whose dynamics are described by polynomials, a method based on semi‐definite programming is proposed to estimate an invariance kernel with target as large as possible by iteratively searching for Lyapunov‐like functions. The proposed methodology is scalable, since the size of the semi‐definite programming problem to be solved grows linearly with the system dimension. We test the method on two interesting examples and compare them with some existing methods, the results show that our method is more efficient.