Adaptive control of nonlinear systems with a triangular structure

Abstract

In this paper, we introduce two distinct types of nonlinear dynamical systems, 풯1 and 풯2, both of which possess a triangular structure. It is shown that all systems belonging to 풯1 can be made stable and that if they belong to a subclass 풯1s, the stability holds globally. A precise characterization of the general class of nonlinear systems transformable to 풯1 is carried out. The second class, 풯2, corresponds to a set of second-order nonlinear differential equations and is motivated by problems that occur in mechanical systems. It is shown that global tracking can be achieved for all systems in 풯2. A constructive approach is used in all cases to develop the adaptive controller, and both stabilization and tracking are shown to be realizable. Simple examples are given to illustrate the different classes of nonlinear systems as well as the idea behind the approach used to stabilize them