Adaptive continuous higher order sliding mode control

This paper is concerned with the development of an adaptation structure which can be applied to conventional, super-twisting and higher-order sliding mode schemes. The objective is to alter the modulation gains associated with these schemes in such a way that they are as small as possible to mitigate chattering effects, but large enough to ensure that sliding can be maintained in the presence of bounded and derivative bounded uncertainties. In all the proposed schemes, the equivalent control is used to drive the adaptive mechanism. The approach is based on a novel dual layer nested adaptive methodology which is quite different to the existing schemes proposed in the sliding mode literature. The new adaptive schemes do not require knowledge of the minimum and maximum allowed values of the adaptive gain, and in their most general form, do not require information about the bound on the disturbances and their derivatives.