Adaptive neural quantized control for fractional-order full-state constrained non-strict feedback systems subject to input fault and nonlinearity

In this work, an adaptive neural network (NN)-based quantized fault-tolerant controller (FTC) has been designed for incommensurate fractional-order (FO) nonlinear systems (NSs) in the non-strict feedback form subject to independent asymmetric time-varying full-state constraints, input quantization, unknown dynamics, infinite number of actuator faults and unknown input nonlinearities. It is assumed that the controller communicates with the actuator via a network with limited bandwidth. To avoid network congestion, the control signal is first quantized by an asymmetric hysteresis quantizer (HQ), then transmitted to the actuator via the network. By incorporating the backstepping algorithm, barrier Lyapunov functions (BLFs) and fractional direct Lyapunov stability (FDLS) theorem, a novel method has been proposed to design a control scheme for FO state constrained NSs and establish the closed-loop stability. In this method, the Lyapunov function of each step of the backstepping algorithm is chosen based on the BLF and parameter estimation error of the considered step and their boundedness is shown from the last step to the first one. Under the proposed control approach, the full-state constraints are met, the tracking error can be made small by selecting proper design parameters and all closed-loop signals remain bounded. Finally, three simulation examples have been provided to demonstrate the designed controller effectiveness.