A decentralized indirect adaptive control for a class of two-time-scale nonlinear systems with application to flexible-joint manipulators

In this paper, the problem of an indirect adaptive decentralized control for a class of two-time-scale interconnected systems is considered. The concept of an integral manifold is first utilized to construct the dynamics of corrected slow subsystems. Fast subsystems are also constructed to represent the dynamics of the fast modes. A composite control scheme based on full state feedback is then developed to guarantee stability and robustness of the closed-loop system. The controller is designed by taking into account the effects of unmodeled dynamics, identification errors, and parameter variations. Stability analysis of the resulting closed-loop full-order system subject to the composite controller is presented. To demonstrate the application of the proposed algorithm, an example of a two-link flexible-joint manipulator is considered. Simulation results are provided to validate the applicability of the proposed control scheme.