A Novel Fractional-Order Second-Order Sliding-Mode Control for Nonlinear Systems Under Matched and Mismatched Uncertainties

To overcome traditional limitations in handling complex disturbances, a novel fractional-order second-order sliding mode control (FOSOSMC) is developed for a class of nonlinear systems in the presence of matched and mismatched uncertainties, ensuring the properties of stability and dynamic performance. The main novelties are highlighted as follows. Firstly, a structurally flexible continuous SOSMC manifold incorporating FO calculus is constructed by taking into account the design of a family of sliding variables, which ensures that the state trajectory can converge to the equilibrium point accurately in a finite time and address the chattering problem owing to its memory and hereditary properties, while uniformly compensating for mismatched uncertainties. Furthermore, the straightforward sliding manifold structure allows for diverse designs of control laws. For simple single-input single-output systems, their fast convergence and high precision under lumped uncertainties can be guaranteed by combining the FOSOSM manifold and a fast-terminal sliding mode-type reaching law. For complex multi-input multi-output systems, a state-dependent adaptive gain is fitted to the FOSOSM manifold to obtain stronger robustness without sacrificing control accuracy or complicating parameter tuning. The global finite-time stability of the closed-loop dynamics is demonstrated by means of Lyapunov functions. Finally, simulation and experimental results verify the excellent control performance of the proposed method for nonlinear systems with uncertainties.