Fully Adaptive Terminal Sliding Mode Control for a Class of Nonlinear Systems With Structured and Unstructured Uncertainties: Theory and Applications

This article introduces a fully automated, continuous nonsingular terminal sliding mode (TSM) control technique to control uncertain, nonlinear, and time-varying second-order systems with both structured and unstructured uncertainties. This proposed TSM control approach is not only continuous, chattering-free, and finite-time stable but also eliminates the necessity of offline identification of the system dynamics and of any assumptions about the upper bounds of the uncertainty. In most practical applications, estimating these boundaries is difficult and challenging. Consequently, large values are chosen and assigned to the control gains to guarantee finite-time convergence. Nevertheless, overestimating the controller gains increases chattering and results in noticeable performance degradation. In this article, TSM-based adaptive laws are proposed for estimating the upper bound of the uncertainties. Moreover, TSM-based control law is proposed such that the finite-time convergence is guaranteed. To evaluate the efficacy of the proposed method, it is applied for the control of an uncertain two-link rigid robotic manipulator as well as for the regulation of admittance and cadence in a real motorized functional electrical stimulation (FES) cycling system. The simulation and experimental studies corroborate that the proposed strategy can provide favorable control performance without chattering under system parameter variations and unknown bounded disturbances.