Iterative designs of adaptive controllers for systems with nonlinear integrators

The authors extend the idea of iterative design of a globally stabilising adaptive controller introduced by I. Kanellakopoulos, P.V. Kokotovic and A.S. Morse (1990). By giving an interpretation of the scheme of Kanellakopoulos et al. in terms of the control Lyapunov function technique, the authors show that it can be applied to a slightly broader family of systems than the strict feedback systems. By noticing that this design involves implicitly at each step a matching condition which is known to hold not only for one integrator but also for two integrators, they propose an adaptive controller with, in general, half as many parameters to update. A significant aspect of these designs is that, together with an adaptive controller, they result in a corresponding control Lyapunov function