Adaptive neural fault-tolerant consensus control of discrete-time fractional-order multi-agent systems for smart energy networks

This paper investigates leader-following consensus for discrete-time fractional-order multi-agent systems with unknown nonlinear dynamics, bounded disturbances, and actuator faults arising in distributed smart energy applications. An adaptive neural-assisted fault-tolerant controller is developed by combining a Caputo-type fractional-order sliding variable with an online Radial Basis Function Neural Network (RBFNN). The RBFNN approximates the unknown nonlinear dynamics, while an adaptive weight-update law compensates {for} the neural approximation error. Actuator degradation is represented through a bounded loss-of-effectiveness factor and additive fault bias, allowing the controller to accommodate different actuator-fault conditions without requiring their exact profiles. A discrete fractional{-order} Lyapunov analysis is established to derive sufficient conditions ensuring {the} boundedness of the sliding variable, {the} neural-weight estimation error and {the} closed-loop signals. The consensus dynamics are subsequently characterized through the stable fractional{-order} error system driven by the vanishing sliding variable. Numerical simulations involving actuator degradation, external disturbances, parameter sensitivity, network scalability{,} and comparative benchmarks demonstrate the effectiveness of the proposed method in reducing consensus error and maintaining coordinated leader-following behavior under uncertain operating conditions.