Nested adaptive integral terminal sliding mode control for high-order uncertain nonlinear systems

This paper aims to develop a nested adaptive integral terminal sliding mode control scheme for high-order uncertain nonlinear systems. To achieve this goal, a recursive-structure integral terminal sliding mode (ITSM) is presented, which consists of a nonsingular terminal sliding mode and a fractional power integral terminal sliding mode. Based on the ITSM, the reaching phase is eliminated and simultaneously, the system is stabilized in finite time. Moreover, due to the full-order sliding mode inherent in ITSM, the reaching control input is obtained in an integral form instead of a signum function. To remove the needs for the upper bounds of the disturbance or its derivatives, a nested dual-layer adaptive law is introduced to update the level of the control gain according to the disturbance variations without overestimation. Stability analysis demonstrates that under the proposed control, the system state starts on the sliding surface and then converges to the origin in finite time in the presence of system uncertainties. The novelty of the proposed method lies in its finite-time origin convergence without reaching phase, nonoverestimation, nonsingular and chattering-free control signal, and those properties have not yet been achieved by any other existing methods. A simulation example is provided to illustrate the superiorities of the proposed control by comparison to conventional method.