Adaptive Fuzzy Fault Tolerant Control for Robot Manipulators With Fixed-Time Convergence

Nonsingular fixed‐time fault‐tolerant control for multiple Euler–Lagrange systems without continuous communication

“…Remark 3. From (28), one knows that the bound of final consensus error is mainly governed by parameters 𝛾 5 , 𝛾 6 and , whose detailed expressions can be found in (27). More specifically, three parameters 𝛾 5 , 𝛾 6 and  are mostly affected by control gains and physical system parameters 𝜌 u , c 1 and a i , that is, final consensus error can be reduced by adjusting control gains.…”

“…[24][25][26] Adaptive fault-tolerant control schemes with fixed-time convergence for single Euler-Lagrange system have been proposed. 27,28 For multiple Euler-Lagrange systems (MELSs), several kinds of fixed-time coordination control algorithms were presented for leader-followers or leaderless consensus problem. 29,30 In view of actuator faults, the authors in Reference 31 proposed the fixed-time fault-tolerant consensus algorithms for MELSs subject to model uncertainties, with the requirement of bounds of faults.…”

“…Moreover, the introduction of fixed-time control complicates the design of control algorithms and brings a new problem (i.e., singularity problem). It should be noted that the singularity problem widely existing in the literatures (see References 13,15,26,[28][29][30]32) is a non-negligible problem for finite-and fixed-time control due to the presence of fractional order in the sliding mode and may cause the instability of the system. Recognizing this limitation, different sliding mode control approaches based on piecewise functions have been developed to address this issue, 27,31,33 but it leads to the problems of discontinuous switching and the errors cannot reach zero.…”

“…Besides, the physical system are susceptible to different uncertainties and failures of devices in a real complicated environment, such that it is of practical significance to investigate this kind of typical physical system 24‐26 . Adaptive fault‐tolerant control schemes with fixed‐time convergence for single Euler–Lagrange system have been proposed 27,28 . For multiple Euler–Lagrange systems (MELSs), several kinds of fixed‐time coordination control algorithms were presented for leader‐followers or leaderless consensus problem 29,30 .…”

“…To illustrate the proposed algorithm's generality, it is further extended to address the saturation constraints problem. A nonsingular adaptive fixed‐time control framework is firstly established for MELSs by introducing an auxiliary system. In contrast to References 26,28‐30,32, the proposed framework avoids singularity and does not require the upper bounds of uncertainties and RVI for MELSs so that the reliability of the system is guaranteed. This paper presents an error decomposition approach for the consensus of MELSs without continuous communication. Compared with the works, 38,39 the fixed‐time intermittent communication scheme can significantly save network resources while ensuring fixed‐time convergence, and does not involve initial conditions, such that it can be served as a more general method.…”