Stabilization of An Underactuated Rigid Body Using Certainty Equivalence Adaptive Control

In this paper, adaptive asymptotic stabilization of angular velocities of a rigid body with two controls is investigated, to provide a solution to such a problem and to give a study of certainty equivalence adaptive control. A control scheme, which leads to asymptotic velocity regulation to zero, is made adaptive, based on the certainty equivalence principle, to handle parameter uncertainties. Such an adaptive control law however cannot ensure asymptotic zero regulation anymore. A redesigned control scheme is presented which has stronger stabilization properties and whose adaptive version is able to achieve asymptotic zero regulation. Observation, analysis, and comparison and simulation results are given, to illustrate that desired performance of certainty equivalence adaptive control is based on certain conditions which may not be satisfied for some nonlinear control systems.