In this chapter, by integrating pseudo-PID sliding-mode control (SMC) method with adaptive control techniques, two innovative fully distributed adaptive fault-tolerantFault-tolerant control schemes are proposed to address the leader-following complete consensusComplete consensus issue in nonlinear multi-agent systems (MASs) under integral quadratic constraints (IQCs) and actuator malfunctions, both with and without asymmetric nonlinear actuator saturationsSaturation (ANASs). For scenarios devoid of saturationsSaturation, the proposed control scheme boasts a straightforward design and minimal computational demands, albeit relying on rudimentary system model details. To address this limitation, in scenarios involving saturationsSaturation, the control scheme is revamped with the incorporation of an innovative anti-windup mechanism and fuzzy logic systems (FLSs), addressing computational complexity reduction. These controllers operate on local interaction data rather than global network data, guaranteeing the practical achievement of complete consensusComplete consensus in leader-follower systems within a finite timeFinite time frame.