Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems
Jiang Liu, Naijun Zhan, Hengjun Zhao
TL;DR
This paper introduces a complete method for automatically discovering relaxed Lyapunov functions for polynomial dynamical systems, enabling better stability analysis through higher order Lie derivatives.
Contribution
It generalizes standard Lyapunov functions to relaxed versions and provides a complete enumeration-based method for polynomial RLF discovery in polynomial dynamical systems.
Findings
Complete method for discovering polynomial RLFs
Able to find all polynomial RLFs for given systems
Utilizes higher order Lie derivatives for stability analysis
Abstract
The notion of Lyapunov function plays a key role in design and verification of dynamical systems, as well as hybrid and cyber-physical systems. In this paper, to analyze the asymptotic stability of a dynamical system, we generalize standard Lyapunov functions to relaxed Lyapunov functions (RLFs), by considering higher order Lie derivatives of certain functions along the system's vector field. Furthermore, we present a complete method to automatically discovering polynomial RLFs for polynomial dynamical systems (PDSs). Our method is complete in the sense that it is able to discover all polynomial RLFs by enumerating all polynomial templates for any PDS.
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Taxonomy
TopicsFormal Methods in Verification · Advanced Control Systems Optimization · Control and Stability of Dynamical Systems