Fractional Order Sliding Mode Control under Non Differentiability and Uncertainty

Abstract

newline This thesis work presents control designs in presence of non-differentiability and uncertainty newlinein systems using fractional-order sliding mode control. The work can be divided into two newlinemain parts. The first part deals with the non-differentiability issues in control problems. In newlinethis context, two problems are considered which are the tracking problem and differentiator newlinedesign problem. The issues occuring due to non-differentiability of some functions in these newlinetwo problems are highlighted. A solution to the problems is proposed by using fractional-order newlineoperators. It is shown how these operators relax the required differentiability condition on the newlinefunctions in case of techniques involving integer-order operators. the second part discusses a newlinesliding mode control based design for a class of uncertain fractional-order systems. The classical newlinefractional-order sliding mode based design cannot guarantee robustness in the reaching phase. newlineIn order to ensure robustness throughout the evolution of the trajectories, a new approach is newlineproposed which is free from the reaching phase. The states are on the sliding surface from the newlinevery beginning achieving the desired robustness