Robust finite non-singular terminal synergetic control for second order nonlinear systems subject to time-varying mismatched disturbances

This paper proposes a novel robust finite synergetic control approach for nonlinear systems subject to time-varying mismatched disturbances. Its main objective is to guarantee the finite-time convergence of the states while eliminating the singularity problem and providing a chattering-free response despite the disturbances. The controller is formulated based on a novel non-singular terminal sliding manifold and the disturbances are estimated using a nonlinear finite time disturbance observer. By estimating the values of the mismatched disturbances and uncertainties, a novel synergetic manifold is introduced which compensates for an estimate of the disturbances. This yields a robust Finite Non-singular Terminal Synergistic Control (FNTSC) that is capable of counteracting the effects of the time-varying mismatched disturbances. System stability is established using the Lyapunov stability theory. The effectiveness and performance of the proposed approach is assessed using a four-bar linkage mechanism as a study case. The obtained results confirmed the robustness, finite time convergence and chattering free dynamics of the proposed controller.