Prescribed fixed-time adaptive fuzzy control for uncertain MIMO nonlinear systems with Preisach operators

For uncertain interconnected MIMO nonlinear systems with Preisach-type hysteresis inputs, the construction of a control strategy such that the fixed-time stability and the presettable steady-state tracking performance can be established simultaneously has not yet been achieved in the existing literature, despite theoretical and practical importance of such a problem. Technically, establishing the fixed-time stability needs the construction of a stringent Lyapunov-based conditional inequality, which is indeed not a trivial task when the existence of interconnection of subsystems, Preisach-type hysteresis inputs, and uncertain unparametrizable nonlinear dynamics, in particular when the predefined steady-state tracking accuracy needs to be established at the same time. To fill in the gap, and overcome the difficulties, in this paper, we propose a novel adaptive fuzzy control approach, for which a robust adaptive framework is developed to accommodate hysteresis nonlinearities and plant dynamics, and a smooth functions-based backstepping design is presented to construct a scheme capable of achieving the desired system performances. With our approach, it can be proved that all signals in the closed-loop system are bounded, and the tracking error for each subsystem converges to the predetermined interval in fixed time. Simulation and experimental tests are conducted to confirm the obtained results.