Adaptive stable control of manipulator system based on immersion and invariance

Abstract

This work focused on the manipulator system containing uncertainties, and proposes an immersion and invariance (I&I) control strategy, in order to avoid the damage on the mechanical and the operation object caused by parameter uncer- tainty. A stable target system with lower dimension than the manipulator system was chosen to design the control law and estimation laws of uncertain parameters. Then finding an invariant and attractive manifold in state space with internal dy- namics a copy of the desired closed-loop dynamics. Finally, design a control law that can steer the state of the system suficiently close to the manifold. The immersion and invariance adaptive control does not rely on certainty equivalence. The whole uncertain parameter estimations are the sum of two terms. One is obtained by an iterative law like the traditional adaptive backstepping method. On the other hand, a nonlinear function is introduced. The role of this additional term makes the param- eter estimations more exible and effective. Lyapunov function is not necessary for the process of designing adaptive controllers. So immersion and invariance can e ec- tively avoid the 'computing expansion' of backstepping method. Compared with the traditional adaptive methods, simulation results show that the proposed immersion and invariance adaptive controller can improve the system performance, including dynamic response, stability and accuracy of parameter estimations.