Finite-time sliding-mode tracking control of uncertain chaotic systems in the presence of an external disturbance and an input saturation

The study presents a Finite-time Sliding-mode Tracking Control (FSTC) technique to achieve the trajectory tracking of an uncertain chaotic system. The feature of the proposed control strategy possesses a high level of robustness even when the uncertain chaotic system is in the presence of external disturbances and input saturation. First, a nonlinear sliding surface with a fractional-order term is constructed using tracking errors so that the finite-time convergence of tracking errors can be attained. The design of the nonlinear sliding surface, i.e. the selection of control parameters, can shape the system response. Since chattering will result from such control design, a boundary layer is adopted in the controller design to mitigate the high-frequency switching of control signal inputs. The overall system stability and finite-time convergence of the tracking error are verified using Lyapunov stability criteria and the relevant lemma. Finally, the proposed FSTC is applied to the Genesio chaotic system in the presence of uncertainty, external disturbance, and input saturation. The simulation results reveal that the proposed control scheme is indeed feasible and effective for chaotic systems control.