Robust observer with sliding mode estimation for nonlinear uncertain systems

To handle the state estimation of a nonlinear system perturbed by a scalar disturbance distributed by a known nonlinear vector, we incorporate a sliding mode term into a nonlinear observer to realise a robust nonlinear observer. By linking the observability of the unknown input to the output measurement, the so-called matching condition is avoided. The measurable output estimation error is the sliding surface. In the sliding mode, the reduced-order error system is free from the disturbance, and the convergence of the estimation error dynamics is proven. The unknown input/disturbance is estimated from the sliding mode. Under a Lipschitz condition for the nonlinear part, the nonlinear observers are designed under the structural assumption that the system is observable with respect to any control input. The proposed robust nonlinear estimator is applied to state and unknown input estimation of a bioreactor. The simulation results demonstrate the effectiveness of the proposed method.