Distributed Event-Triggered Adaptive Formation Tracking of Networked Uncertain Stratospheric Airships Using Neural Networks

Abstract

This paper investigates a distributed event-triggered formation tracking problem of networked three-dimensional uncertain nonlinear stratospheric airships under directed networks. It is assumed that the nonlinearities of airship followers are unknown and the leader information can be obtained by only a subset of the airship followers. Approximation-based local adaptive tracking controllers with asynchronous event-triggering laws are developed to achieve the desired formations for both the positions and attitudes of uncertain stratospheric airship followers. We theoretically show that the stability and formation tracking performance of event-triggered closed-loop systems are ensured and Zeno behavior is excluded in the proposed asynchronous event-triggering mechanism. Finally, simulations illustrate the effectiveness of the proposed formation control protocol. INDEX TERMS Distributed adaptive formation tracking, event-triggered, neural networks, networked stratospheric airships.

Quantized-Feedback-Based Adaptive Event-Triggered Control of a Class of Uncertain Nonlinear Systems

“…Consider the uncertain strict-feedback nonlinear system (1) with the uniform state quantizer (2). Then, for any initial conditions satisfying V(0) ≤ ς, the quantized-feedback-based adaptive event-triggered tracker consisting of the command filters (17) and (23), the virtual control laws (14), the actual event-triggered control law (18)- (20) with the adaptation laws (15), (16), (21) and (22) ensures that all the closed-loop signals are uniformly ultimately bounded, the tracking error µ 1 converges to an adjustable compact set around zero, and the inter-event times t l+1 − t l are lower bounded by the minimum inter-event time t min > 0 where l ∈ Z + .…”

“…However, the quantized feedback control laws reported in [13,14] were not differentiable because of the quantized state variables. To overcome this problem, we employ the auxiliary first-order low-pass filter (23) for the quantized-feedback-based control law α q n in (20). Subsequently, the differentiable signalα q n,1 is used in the event-triggered actual control law u in (18).…”

“…Unlike the conventional time-triggered strategy, an event-triggered strategy can reduce the amount of computation and communication resources required in networked control systems. Owing to these advantages, some event-triggered control methods were presented for linear and nonlinear networked control systems [17][18][19][20]. For lower-triangular nonlinear systems with parametric uncertainties, Xing et al [21] first suggested an adaptive recursive event-triggered control approach using three types of thresholds.…”

Event-Triggered Dynamic Coverage Control for Multiple Stratospheric Airships

“…Owing to the rapid development of solar energy and material technology, the stratospheric airship has become a research hotspot in recent years thanks to its ability to perform tasks aloft or hovering around a specified area at the altitude of around 20 km [ 2 ]. Control research on the stratospheric airship includes path following [ 3 , 4 ], trajectory tracking [ 5 , 6 ], station keeping [ 7 , 8 , 9 ], formation tracking [ 10 , 11 , 12 ], and so on. As a high-altitude platform that can perform tasks in a fixed area for a long time, the demand for area coverage control is very strong.…”

“…First, several examples of recent research are cited for the control field of the MSA system as follows. In [ 10 ], the distributed event-triggered formation tracking problem of the MSA system with unknown nonlinearities was investigated. The adaptive fault-tolerant formation-containment control of the MSA system with input saturation was addressed in [ 11 ].…”