Adaptive regulation: Lyapunov design with a growth condition. (English) Zbl 0769.93068
Summary: 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 nonlinearities. We show it is satisfied by strict pure feedback systems with polynomial growth nonlinearities 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.
MSC:
| 93D21 | Adaptive or robust stabilization |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
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