Whole-Process Predefined-Time Tracking Control for T–S Fuzzy Euler–Lagrange Systems

This article realizes whole-process predefined-time tracking control in Takagi–Sugeno (T–S) fuzzy Euler–Lagrange systems with zero-error through the proposed novel nonsingular sliding-mode- and observer-based (NSMOB) control algorithm. Under the supplementary of the sliding mode (SM) and extended state observer (ESO), the antidisturbance and fitting unknown smooth function abilities for the control algorithm is further promoted. And more importantly, the complex problem of nonsingular predefined-time control with zero-error in second-order systems is uniquely addressed by a newly nonsingular whole-process predefined-time controller, which forms NSMOB control algorithm, combined with the existing predefined-time SM and predefined-time ESO. Furthermore, the theoretical rationality of the NSMOB control algorithm is proven creatively and rigorously with the help of the Lyapunov function and several sufficient criteria. And eventually, the control algorithm is applied to a two-link robot manipulator to validate its effectiveness and superiority over the existing nonsingular predefined-time control algorithm.