Adaptive Finite-Time Control for Multi-Input Multi-Output Nonlinear Systems with Input Saturation and External Disturbances

This work presents a finite-time adaptive fuzzy control approach for a category of multi-input multi-output nonlinear systems in the presence of input saturation and external disturbances. A hyperbolic function is adopted to convert the unconstrained control command into a bounded signal so that the actuator constraints are strictly respected. Unknown nonlinearities are approximated by fuzzy logic systems, whereas external disturbances are attenuated by adaptive mechanisms together with tanh-based robust terms. In addition, dynamic surface control is incorporated into the backstepping framework, where first-order filters are employed to avoid the computational burden associated with the repeated differentiation of virtual control laws. On this basis, a Lyapunov-based design is carried out to derive the finite-time adaptive control protocol. It is shown that every signal in the resulting closed-loop system is bounded, the closed-loop system is semi-globally practically finite-time stable, and the state variables converge to a small neighborhood of the desired states within a finite settling time, and the control inputs never exceed the prescribed bounds. Simulation results obtained using a representative rigid spacecraft as an example confirm the feasibility and disturbance-rejection capability of the developed method.