Analysis and Comparison of Iterative Bilinear Sum-of-Squares Region of Attraction Estimation Algorithms

12/15/2022

A common system-theoretic problem for critical nonlinear dynamical systems such as aerospace systems is the estimation of the region of attraction. A well known approach to the problem relies on Lyapunov functions and invariant sets. Several strategies using sum-of-squares relaxations and semi-algebraic optimizations have been proposed, but a comparison of those strategies on benchmark problems and a detailed characterization is lacking. Properties such as convergence, robustness to initial guesses, computational issues and scalability have not been studied in a clear way. So in this thesis, a set of problems is presented which builds up a proposed test bench where different algorithms are to be characterized, compared and tested, and where all those properties can be extracted. Results from the most known and recent algorithms in the literature are presented as an application of the test bench, alongside a new proposal involving the use of two adaptive shape functions. Additionally, a proposal to estimate the region of attraction through an iterative sum-of-squares approach is presented but in contrast with the current literature, it is not based on Lyapunov theory but instead on the Bendixson-Dulac criterion for planar dynamics and set invariance. Also, extensions for higher dimensional systems are presented and discussed.

Authors in the community:

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  R

  Renato Bastos Loureiro

  ist189708

Supervisors of this institution:

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  R

  Rita Maria Mendes de Almeida Correia da Cunha

  ist31057

mechanical-engineering - Mechanical engineering

eng - English

Instituto Superior Técnico