Composite observer-based adaptive event-triggered backstepping control for fractional-order nonlinear systems with input constraints

An event-triggered neural adaptive backstepping controller via a state and a disturbance observers is proposed for uncertain fractional-order nonlinear systems with time-varying external disturbances and unavailable states. The radial basis function neural network (RBFNN) is utilized to approximate uncertain nonlinear terms, and a coupled observer including both state observer and disturbance observer is developed in view of the output of the RBFNN to obtain the dynamic information of unmeasured states and unknown compounded disturbances. Then, to tackle with the impact of input constraints, an auxiliary system is constructed, and an event-triggered approach is developed to cut down communication burden between the controller and the actuator. Moreover, a dynamic surface control strategy is developed to cope with the tedious analytic computation of time derivatives of virtual controllers. The stability analysis demonstrates that the involved signals remain bounded, and tracking and observering errors can converge to a diminutive neighborhood around the origin. At last, the effectiveness of the developed control method is verified by two numerical examples.