Hybrid observer-based fixed-time tracking control for constrained nonlinear systems

This paper introduces a hybrid observer-based fixed-time tracking control for constrained nonlinear systems. Multiple factors constrain the considered nonlinear systems: internally by dynamic uncertainties and full-state constraints, and externally by external disturbances, actuator faults, and input saturation. A hybrid observer, combining the bias RBFNN (radial basis function neural network) with fixed-time sliding mode, is proposed. The bias RBFNN approximates dynamic uncertainties, while an extended state is designed to estimate the network approximation error, external disturbances, and actuator faults and feed them back to the controller within a fixed time. Meanwhile, the hybrid observer can acquire the velocity information simultaneously. To prevent system states from exceeding predefined boundaries, a barrier function-based state transformation method is implemented. An anti-windup compensator is designed to mitigate the adverse effects caused by input saturation. The semi-globally ultimately fixed-time boundedness (SGUFTB) of the closed-loop system is proven through Lyapunov theory. The effectiveness of the proposed control strategy is demonstrated through simulation and comparative results.