Lai, Brian: Novel Algorithms for Nonlinear Stability Analysis with Applications to Aircraft Dynamics
Title: Novel Algorithms for Nonlinear Stability Analysis with
Applications to Aircraft Dynamics
Name: Brian Lai
Major: Mechanical and Aerospace Engineering
School affiliation: School of Engineering
Programs: James J. Slade Scholars Program
Other contributors: Laurent Burlion
Abstract: We propose extensions to a method for estimating the region
of attraction (ROA) of nonlinear ODE systems based only on measurements of convergent trajectories. We extend the ROA estimation technique to ODE systems with finitely many trim points, and to ODE systems with an arbitrary set of trim points. Additionally, we propose two novel techniques to improve the rate of convergence to the true ROA. The first technique is to partition each convergent trajectory into several trajectories for faster estimation convergence. The second is guaranteeing that divergent initial conditions are outside the estimated region of attraction by adding additional constraints to the estimation algorithm. These tools are used to analyze the longitudinal stability of the NASA GTM scale aircraft, in particular the capability of a given control strategy to return the aircraft to linear dynamics. In this analysis, we show the feasibility of this ROA estimation strategy in a problem of dimension four.