Adaptive control of a class of nonlinear systems with a triangular structure

An adaptive control approach to a class of nonlinear systems with a triangular structure is developed. The systems considered here are described by a set of second-order differential equations, and thus there are many applications to the control of mechanical systems. The design procedure of the control law is based on the idea of properly using the structure of the system, and sequentially developing an adaptive controller that is globally stable. A class of single-input single-output nonlinear systems with a triangular structure is defined and the stabilizability conditions are derived. A control strategy to stabilize the same class of systems with unknown parameters is developed and an adaptive controller for realizing the strategy is systematically designed. The constructive procedure used for generating the adaptive controller is shown to result in the closed-loop system being asymptotically stable at the origin. The approach is illustrated using an example of a coupled mechanical system