Robust Lyapunov control with perturbation estimation

This paper studies a new approach for robust motion control of nonlinear systems with uncertain dynamics and unknown disturbances. The skeleton of the approach is a variable structure controller (VSC) with a nonsliding regime. Due to the nonsliding feature the control is free from high frequency oscillations (typical of sliding mode control), which makes the proposed approach very attractive. Negative definiteness of a Lyapunov function is assured everywhere in the state space except within a problematic strip. A robustising remedy is provided to resolve this dilemma. This is achieved by appropriate selection of the control parameters. The uncertainties primarily arise from parameter variations and imprecise dynamic models, all of which are lumped into `perturbations´. Robustisation against these `perturbations´ is obtained using their estimators within the control. The upper bounds of the perturbations themselves do not have to be known a priori to the control. Instead, the supremum of the errors in estimating these perturbations is required. That is, the conventional requirement of uncertainty bounds are shifted from the actual perturbations to the quality of their estimators. An off-line procedure for determining these estimation error bounds is given. They display a strong dependence on control hardware at hand. Example simulations are given on a two-link manipulator