Adaptive prescribed-time control for time-varying full-state-constrained nonlinear stochastic systems with actuator failures

In this paper, the problem of prescribed-time adaptive fuzzy tracking control for a class of time-varying full-state-constrained nonlinear stochastic systems with actuator failures is considered. Using a unified barrier function in place of the traditional barrier Lyapunov function (BLF) allows for the transformation of nonlinear stochastic systems with time-varying full-state constraints into equivalent ‘unconstrained’ systems for processing, which can eliminate the feasibility condition required by the virtual controllers generated using the BLF approach. The problem of unknown control gain caused by actuator failures is solved via devising reasonable adaptive laws. At the same time, a prescribed-time tracking controller is devised by using the approximation ability of fuzzy logic systems, which can adapt to the uncertainty of the system and deal with the actuator failures. In addition, the control scheme proposed in this paper can guarantee the performance of the system within prescribed-time and all state variables do not violate the constraint boundaries despite suffering from actuator failures. Finally, the effectiveness of the investigated control strategy is verified through two simulation examples.