Fuzzy Adaptive Backstepping Control of Nonlinear Uncertain Systems with Unmeasured States and Input Saturation

Abstract

Considering the uncertainties caused by multiple concurrent complex environments, we investigate the robust adaptive control of multi-source uncertain systems under unmeasurable states and input saturation. For the unmeasurable states caused by sensor faults, a state observer is proposed to provide state estimation values for the controller; for the compound uncertain functions composed of nonlinear uncertain parameters and environmental disturbances, an optimal fuzzy approximation strategy is designed to reproduce these uncertain functions. Finally, the state observer with optimal approximation errors is proved to be stable. Subsequently, the low-pass filter, dynamic surface, and backstepping joint control scheme ensures the robust stability of the uncertain systems, while avoiding the differential explosion caused by disturbances. A series of hierarchical adaptive laws enable the controller to adjust parameters to achieve an optimal tracking of the entire process of time-varying reference output. The compensation algorithm designed with a Nussbaum function solves the problem of input saturation caused by actuator faults. Finally, the nonlinear uncertain systems based on fuzzy adaptive backstepping achieve robust tracking control of time-varying signals. The stability is proved by Lyapunov functions, and the effectiveness of the method simulation is verified using hypersonic vehicle model as an example.