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Location
College of Science and Mathematics (COSM)
Session Format
Oral Presentation
Co-Presenters and Faculty Mentors or Advisors
Dr. Yan Wu
Abstract
The progression of state trajectories with respect to time, and its stability properties can be described by a system of nonlinear differential equations. However, since most nonlinear dynamical systems cannot be solved by hand, one must rely on computer programs. There exists a useful tool known as the Lyapunov Exponents (LEs). The LEs give the average rate of separation of nearby orbits in phase space. They can be used to determine the state of a system based on the signs of the LEs. Hence, LEs are perfect indicators for the stability of the state trajectory. The objective of this research is to provide a convenient toolbox designed for studying the stability properties of a large class of control systems that is capable of automatically detecting the stability and instability of a control system.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Presentation Type and Release Option
Presentation (Open Access)
Recommended Citation
Andrews, Nakita, "Numerical Approximation of Lyapunov Exponents and Its Applications in Control Systems" (2021). GS4 Georgia Southern Student Scholars Symposium. 63.
https://digitalcommons.georgiasouthern.edu/research_symposium/2021/2021/63
Numerical Approximation of Lyapunov Exponents and Its Applications in Control Systems
College of Science and Mathematics (COSM)
The progression of state trajectories with respect to time, and its stability properties can be described by a system of nonlinear differential equations. However, since most nonlinear dynamical systems cannot be solved by hand, one must rely on computer programs. There exists a useful tool known as the Lyapunov Exponents (LEs). The LEs give the average rate of separation of nearby orbits in phase space. They can be used to determine the state of a system based on the signs of the LEs. Hence, LEs are perfect indicators for the stability of the state trajectory. The objective of this research is to provide a convenient toolbox designed for studying the stability properties of a large class of control systems that is capable of automatically detecting the stability and instability of a control system.
