Premium
Stabilization of underactuated nonlinear systems to non‐feasible curves
Author(s) -
Grushkovskaya Victoria,
Zuyev Alexander
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900160
Subject(s) - nonlinear system , parameterized complexity , lyapunov function , nonholonomic system , underactuation , mathematics , exponential stability , control theory (sociology) , neighbourhood (mathematics) , trajectory , ordinary differential equation , stability (learning theory) , convergence (economics) , mathematical optimization , computer science , differential equation , mathematical analysis , control (management) , robot , mobile robot , artificial intelligence , physics , combinatorics , quantum mechanics , astronomy , machine learning , economic growth , economics
This paper focuses on the development of stability conditions for systems of nonlinear non‐autonomous ordinary differential equations and their applications to control problems. We present a novel approach for the study of asymptotic stability properties for nonlinear non‐autonomous systems based on considering a parameterized family of sets. The proposed approach allows to state asymptotic stability conditions for a family of sets representing the level sets of a time‐varying Lyapunov function and to estimate the rate of convergence of solutions to a prescribed neighbourhood of the given curve. The obtained stability results are applied to the trajectory tracking problem for a class of nonholonomic systems.