Summary An observer‐based adaptive fuzzy backstepping approach is proposed for nonlinear systems with respect to fractional‐order differential equations, unmatched uncertainties, unmeasured states, and actuator faults. The approximation capability of fuzzy logic system and minimal learning parameter approaches are applied to identify uncertain functions in a simultaneous manner. For estimating the unavailable conditions, a fuzzy fractional‐order state‐observer is extended. Applying fault‐tolerant approach in a backstepping design methodology would provide a new fault‐tolerant adaptive fuzzy output‐feedback approach for fractional‐order strict‐feedback systems. This control structure would assure the considered system stability through selection of the appropriate Lyapunov candidate function. Two numerical simulations are run to exhibit the validity herein.

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This paper proposes a tracking controller for the formation construction of multiple autonomous surface vessels (ASVs) in the presence of model uncertainties and external disturbances with output constraints. To design a formation control system, the leader-following strategy is adopted for each ASV. A symmetric barrier Lyapunov function (BLF), which advances to infinity when its arguments reach a finite limit, is applied to prevent the state variables from violating constraints. An adaptive-neural technique is employed to compensate uncertain parameters and unmodeled dynamics. To overcome the explosion of differentiation term problem, a first-order filter is proposed to realize the derivative of virtual variables in the dynamic surface control (DSC). To estimate the leader velocity in finite time, a high-gain observer is effectively employed. This approach is adopted to reveal all signals of the closed-loop system which are bounded, and the formation tracking errors are semi-globally finite-time uniformly bounded. The computer simulation results demonstrate the efficacy of this newly proposed formation controller for the autonomous surface vessels.

In this article, the one DOF robot manipulator control is assessed through second type robust fuzzy-adaptive controller. The objective is to obtain a tracking path with appropriate accuracy. The stability of the closed loop system is verified through Lyapunov stability theory and the efficiency of tracking is analyzed subject to the constraints and uncertainty. In order to design the fuzzy controller a set of if-then fuzzy rules are considered which describe the system input-output behavior. Simulation and the results of the experiments on the one DOF robots indicate the effectiveness of the proposed methods.

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This paper addresses a new constrained control design problem to develop the trajectory-tracking specifications of the cooperative control of Euler–Lagrange systems with respect to the convergence rate and steady-state errors by constraining the limited bounds on the trajectory-tracking errors in the leader–follower formation control problem. A control design based on an asymmetric barrier Lyapunov function is proposed for the leader–follower formation control of Euler–Lagrange systems in the presence of unknown parameters and unmodeled dynamics that progresses to the infinity when its arguments attain to the predefined bounds. These constrained output states are considered in the leader–follower formation control problem to cope with the system restrictions such as limited sensing ranges. The Lyapunov stability is pursued to assure that all the signals of the closed-loop system are bounded and the leader–follower formation errors are finite-time semi-globally uniformly ultimately bounded. Finally, computer simulation results represent the impression of the newly proposed constrained leader–follower formation control for the Euler–Lagrange systems.