Nonlinear Gliding Stability and Control for Vehicles with Hydrodynamic Forcing
Pradeep Bhatta and Naomi Ehrich Leonard, Automatica, Vol. 44, 2008, 1240-1250.
This paper presents Lyapunov functions for proving stability of steady gliding
motions for vehicles with hydrodynamic or aerodynamic forces and moments. Because of lifting
forces and moments, system energy cannot be used as a Lyapunov function candidate. A Lyapunov
function is constructed using a conservation law discovered by Lanchester in his classical work
on phugoid-mode dynamics of an airplane. The phugoid-mode dynamics, which are cast here as
Hamiltonian dynamics, correspond to the slow dynamics in a multi-time-scale model of a
hydro/aerodynamically forced vehicle in the longitudinal plane. Singular perturbation
theory is used in the proof of stability of gliding motions. As an intermediate step,
the simplifying assumptions of Lanchester are made rigorous. It is further shown how to
design stabilizing control laws for gliding motions using the derived function as a control
Lyapunov function and how to compute corresponding regions of attraction.
(1.2 MB pdf)
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