Higher order sliding modes manifold design via singular LQ control

The paper shows how the solution of Singular Optimal Stabilization Problem (SOSP) for nominal system can be used for the sliding manifold design for higher order sliding mode control (HOSMC) for uncertain system. This paper consists of two main parts. In the first part, the natural connection between the order of singularity of SOSP and the order of sliding mode is established, and as a conclusion it is shown that the Singular Optimal Manifold (SOM) can be considered as the sliding surface for HOSMC of the corresponding order ensuring the sliding modes for uncertain system. In the second part we have designed a feasible curve to arrive to the SOM in prescribed time taking into account actuators limitations. It is shown that integral HOSMC ensures the exact tracking to this curve starting from the initial time moment in spite of uncertainties.