Zh. Li et M. Krstic, MAXIMIZING REGIONS OF ATTRACTION VIA BACKSTEPPING AND CLFS WITH SINGULARITIES, Systems & control letters, 30(4), 1997, pp. 195-207
Citations number
8
Categorie Soggetti
Controlo Theory & Cybernetics","System Science","Operatione Research & Management Science
When a nonlinear control law contains a singularity (that is, becomes
unbounded on a set of points in the state space), the region of attrac
tion is often only a subset of the region of feasibility of this contr
ol law. A method which is well known to suffer from this difficulty is
feedback linearization. We show that the backstepping design (in its
standard form) has an inherent ability to make the regions of feasibil
ity and attraction coincide, thus maximizing the latter. The key obser
vation that this paper provides is that a standard backstepping-style
control Lyapunov function, which grows unbounded on the set where the
control law becomes unbounded, has level sets that always remain in th
e feasibility region, which makes the feasibility region positively in
variant. A simulation comparison with a feedback linearization design
shows a dramatic improvement of the region of attraction with backstep
ping. Since our theorem imposes a strong assumption that the feasibili
ty region for the first subsystem in the backstepping problem is posit
ively invariant, we present examples (ranging from simple to fairly di
fficult) which demonstrate how this condition can be satisfied. (C) 19
97 Elsevier Science B.V.