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Adaptive regulation: Lyapunov design with a growth condition
Author(s) -
Praly Laurent
Publication year - 1992
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480060407
Subject(s) - lyapunov function , lyapunov equation , lyapunov redesign , control theory (sociology) , control lyapunov function , mathematics , lyapunov optimization , regulator , equivalence (formal languages) , adaptive control , polynomial , equilibrium point , nonlinear system , computer science , control (management) , mathematical analysis , differential equation , discrete mathematics , biochemistry , chemistry , quantum mechanics , artificial intelligence , gene , physics
We propose a new Lyapunov design of an adaptive regulator under some restriction on the dependence of a Lyapunov function on the parameters. This restriction has been introduced by Praly et al. Its interest is to involve only a Lyapunov function and not explicitly the system non‐linearities. We show it is satisfied by strict pure feedback systems with polynomial growth non‐linearities and some other non‐feedback linearizable systems. Our new Lyapunov design leads to an adaptive regulator where the adapted parameter vector is transformed before being used in the control law; namely, the so‐called certainty equivalence principle is not applied. Unfortunately, the implementation of this regulator needs the explicit solution of a fixed point problem, so in a second stage we propose a more practical solution obtained by replacing the fixed point static equation by a dynamical system with this fixed point as equilibrium.