Adaptive control of nonlinear systems with a triangular structure

In this paper, we introduce two distinct types of nonlinear dynamical systems, /spl Tscr//sub 1/ and /spl Tscr//sub 2/, both of which possess a triangular structure. It is shown that all systems belonging to /spl Tscr//sub 1/ can be made stable and that if they belong to a subclass /spl Tscr//sub 1s/, the stability holds globally. A precise characterization of the general class of nonlinear systems transformable to /spl Tscr//sub 1/ is carried out. The second class, /spl Tscr//sub 2/, 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 /spl Tscr//sub 2/. 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.>