Fractional integral sliding modes for robust tracking of nonlinear systems

• DOI: 10.1007/s11071-016-3086-5
• Publication Date: 2016-09-19T19:05:14Z
• Authors: Aldo-Jonathan Muñ...; Vicente Parra-Vega; Anand Sánchez-Orta
• Keywords: 0209 industrial biotechnology; 02 engineering and technology

Memory and heritage of differintegral operators require knowledge of the error manifold derivative at the initial time to sustain a sliding motion for any initial condition. Moreover, when the system is subject to (unknown) disturbances, such initial condition is unknown; thus, the enforcement of an integral sliding motion has been elusive with a chatter-less controller. In this paper, a novel fractional-order integral sliding mode (FISM) is proposed to maintain an invariant sliding mode due to an exact estimation of disturbances at first step. Our scheme is continuous after initial condition, avoiding chattering effects thanks to the topological properties of differintegral operators. In contrast to other FISM approaches, the proposed scheme induces a fractional-order reaching dynamics of order $$(1+\nu )\in (1,2)$$ to enforce an integral sliding mode for any initial condition, even in the presence of Holder (continuous but not necessarily differentiable) disturbances and model uncertainties. Simulations show the reliability of the proposed scheme.