Higher Order Sliding Mode Based Accurate Tracking of Unmatched Perturbed Outputs

Three approaches for higher-order sliding-mode based unmatched uncertainty compensation are summarized. Firstly, an algorithm is proposed based on the block control and quasi-continuous higher order sliding modes techniques. This method provides for the finite-time exact tracking of a smooth desired signal in spite of unmatched perturbations and allows the reduction of the controller gains in the case of partial knowledge of the system model. Thereafter, the combination of integral high-order sliding modes with the hierarchical quasi-continuous controller is proposed allowing finite-time convergence theoretically. Finally, high-order sliding mode observers are employed for exact state and uncertainties/perturbations reconstruction. A sliding mode control design is proposed which ensures theoretically exact compensation of the uncertainties/perturbations for the corresponding unmatched states based on the identified perturbation values. An inverted pendulum simulation example is considered for illustrating the feasibility of the proposed approach.