Robust adaptive control for robotic systems with input time-varying delay using Hamiltonian method

This paper addresses the problem of robust adaptive control for robotic systems with model uncertainty and input time-varying delay. The Hamiltonian method is applied to develop the stabilization results of the robotic systems. Firstly, with the idea of shaping potential energy and the pre-feedback skill, the n degree-of-freedom ( DOF ) uncertain robotic systems are realized as an augmented dissipative Hamiltonian formulation with delay. Secondly, based on the obtained Hamiltonian system formulation and by using of the Lyapunov-Krasovskii ( L-K ) functional method, an adaptive controller is designed to show that the robotic systems can be asymptotically stabilized depending on the input delay. Meanwhile, some sufficient conditions are spelt out to guarantee the rationality and validity of the proposed control law. Finally, study of an illustrative example with simulations shows that the controller obtained in this paper works very well in handling uncertainties and input delay in the robotic systems.