Adaptive hybrid type-2 intelligent sliding mode control for uncertain nonlinear multivariable dynamical systems

A new adaptive hybrid interval type-2 fuzzy neural network (FNN) controller incorporating sliding mode and Lyapunov synthesis approaches is proposed in this paper to handle the training data corrupted by noise or rule uncertainties for a class of uncertain nonlinear multivariable dynamic systems. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an output feedback control law and adaptive laws, is a combination of interval type-2 indirect and direct adaptive FNN controllers to meet the requirement of sufficient reach for the sliding mode control. A weighting factor, which can be adjusted based on the trade-off between plant knowledge and control knowledge, is included when combining the control efforts of the indirect adaptive FNN controller and the direct adaptive FNN controller. The overall adaptive control scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. The mass–spring–damper nonlinear system is fully illustrated to track sinusoidal signals. The resulting adaptive hybrid interval type-2 FNN control system shows better performance than the adaptive hybrid type-1 FNN control system; it reduces both the tracking error and the control effort and it is more flexible in the design process.