In this work, a lower limb exoskeleton with uncertainties and external disturbances under constrained motion has been controlled by developing a model‐free adaptive optimal fractional‐ordersuper‐twisting sliding mode (AOFSTSM) controller. Contrary to popular existing modeling methods, the modeling of the lower limb exoskeleton has been accomplished in the case of contact with the ground. A fractional‐order operator and super‐twisting sliding mode control have been combined to achieve an excellent tracking performance, chatter‐free control inputs, and robustness to external disturbances and uncertainties. The controller structure is model‐independent which has been derived without needing to know the dynamics of the system. An adaptive control strategy has been adopted as an approximating method to evaluate the uncertain dynamics of the system without the necessity for knowing the prior knowledge of the upper bounds. A grey wolf optimization technique has been used to find the optimal values of controller parameters. The stability of the overall system has been investigated and derived from the Lyapunov stability criterion. To validate the effectiveness of our proposed controller structure, a series of comparative simulations have been conducted with optimal fractional‐order super‐twisting sliding mode (OFSTSM) controller and fractional‐order super‐twisting sliding mode (FSTSM) controller. The comparative simulations have been also carried out with other types of recently existing control methods and recently existing optimization algorithms. The results of numerical simulations indicate the superiority of the AOFSTSM controller over other types of recently existing optimization algorithms and controllers in terms of tracking error and robustness towards the uncertainties and external disturbances.

This research addresses the intricate challenges of fault estimation (FE) and fault-tolerant control (FTC) within a specific subset of T-S fuzzy systems. These systems are characterized by their localized nonlinear models, the presence of unknown inputs, actuator imperfections, and disruptive output disturbances, making them fertile ground for exploration in this study. The contributions of this paper can be summarized as follows: (1) First, we employ coordinate transformation matrices to convert the T-S fuzzy model. This transformation separates the unknown inputs and disturbances at the output. Subsequently, we equip the modified system with a T-S fuzzy adaptive sliding mode observer (ASMO) that serves the dual purpose of fortifying resilience against disruptions and adeptly deducing an extensive spectrum of fluctuating actuator failure signals. (2) In the next step, the insights gained from FE are harnessed to craft a dynamic fuzzy output feedback fault-tolerant controller (DOFFTC). This controller aims to mitigate the effects of actuator errors to maintain the stability of the closed-loop system. The article creates the necessary conditions for the presence of the required ASMO and DOFFTC using H-infinity filtering methods. To address the optimization issue posed by these criteria, we utilize linear matrix inequalities (LMIs) and calculate the required gains for implementation using convex optimization techniques. (3) The study concludes by illustrating the applicability of the proposed techniques with an example employing an inverted pendulum. This paper presents a comprehensive approach to overcoming the challenges of FE and FTC within T-S fuzzy systems. It leverages precise mathematical formulations and optimization strategies to achieve resilient and dependable control, even when confronted with intricate system dynamics.