A Distributed Adaptive Mixed Self-/Event-triggered Formation Control Approach for Multiple Stratospheric Airships with Relative State Constraints and Input Delay

This paper investigates the distributed formation control problem of multiple stratospheric airships in three-dimensional space with several practical problems, such as relative state constraints, input delay, input saturation and disturbances. An adaptive mixed self-/event-triggered formation control scheme is proposed by combining backstepping control, an adaptation technique and a mixed self-/event-triggered control mechanism. First, a novel relative-error-constraint virtual control law is designed based on the barrier Lyapunov function, which is processed into the desired velocity and angular velocity as the input of the next-step designed controller. Then, an adaptive controller is designed based on a designed adaptive law that is utilized to eliminate the influence of external disturbances, input saturation and input delay. In addition, a mixed self-/event-triggered mechanism is designed in the whole system, involving a self-triggered mechanism in the virtual control law and an event-triggered mechanism in the adaptive controller. All signals in the closed-loop system are proven to be semiglobal, uniform and ultimately bounded, and Zeno behavior is proven to be excluded. Finally, the effectiveness of the proposed method is verified through simulations.