Towards an adaptive regulator: Lyapunov design with a growth condition

The author studies a growth condition which does not explicitly involve the system nonlinearities and is satisfied by a class of systems encompassing at least the strict pure feedback systems with polynomial growth nonlinearities and parameter vector in a known compact set. A novel Lyapunov design of an adaptive regulator under this condition is proposed. The Lyapunov design leads to an adaptive regulator where the adapted parameter vector is transformed before being used in the control law. Namely, the certainty equivalence principle is not applied. Unfortunately, the implementation of this regulator needs the explicit solution of a fixed point problem