Robust Lyapunov control with perturbation estimation

This paper presents an approach for motion control of nonlinear systems with modeling uncertainties which are called perturbations. These perturbations are estimated online as a compensating mechanism against the unknown terms. The starting point is a Lyapunov function that is dependent only on the joint tracking errors. Then a robust Lyapunov control is found such that the tracking errors are minimized, and ultimately confined to a prescribed manifold. The robustness against uncertain dynamics is treated in length. The convergence is assured outside the manifold in order to form a “reaching phase” from the initial state towards the manifold. An advantage of the method over the conventional sliding mode control is that it is not necessary to have a prior knowledge of modeling uncertainties and disturbance upper bounds. However, it is necessary to determine and assure an upper bound for the estimation errors. Parametric selections for the controller are suggested to obtain the desired tracking performance. Simulation results are presented for a two-link manipulator