The Distributed Adaptive Bipartite Consensus Tracking Control of Networked Euler–Lagrange Systems with an Application to Quadrotor Drone Groups
Abstract
:1. Introduction
- (1)
- This paper examines networked ELSs subject to lumped uncertainties, which encompass unknown system matrices, external disturbances, and actuator faults. A neural-network-based adaptive estimator is proposed to offer feedforward compensation for these uncertainties. Furthermore, adaptive updating laws are formulated to guarantee that the estimation errors associated with the lumped uncertainties and actuator faults are bounded, thereby tackling the robust tracking control challenge. In contrast to existing control strategies tailored for ideal systems [11,12,13,15,24], the most significant novelty of this work is the enhanced robustness of unknown systems, enabling the control scheme to be applicable across a range of tasks, including the cooperative control of ELSs in dynamic and complex environments.
- (2)
- This paper addresses the issue of uncertainties in leader agents, where their higher-order dynamic information is globally unknown. To tackle this challenge, an adaptive distributed observer is utilized to estimate the states, state matrix unknown parameters, and output matrix of the leader agent. The convergence of the observer’s estimates is rigorously proven through Lyapunov function analysis. This approach diverges from related works that presuppose the availability of the leader’s complete dynamic information to the follower agents, such as the state matrix or output matrix [7,11,23,28]. The proposed control scheme’s adaptability enhances its applicability to a wider array of consensus-tracking control tasks, including trajectory tracking in intricate marine environments.
- (3)
- This paper introduces a novel positive definite diagonal matrix to facilitate the construction of a distributed observer. This innovative design effectively addresses the challenge of asymmetric Laplacian matrices inherent in directed graphs, thereby offering a viable solution for bipartite consensus tracking control of ELSs under general directed graph conditions. In contrast to existing control schemes confined to undirected graph scenarios [4,9,14,15,21], the controller proposed herein demonstrates a capacity to conserve communication resources.
2. Preliminaries and Problem Formulation
2.1. Graph Theory
2.2. RBF Neural Network
2.3. Problem Description
3. Neural-Network-Based Control Scheme Design and Analysis
3.1. Distributed Observer Design and Stability Analysis
3.2. Robust Tracking Controller Design and Stability Analysis
4. Simulation Results
4.1. Example 1: Two-Link Robot Manipulator
4.2. Example 2: Quadrotor Drone
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Symbol | Meaning |
---|---|
q | leader’s state |
y | leader’s output |
the leader’s state matrix | |
w | an unknown parameter vector |
E | the leader’s output matrix |
the generalized coordinate, velocity, and acceleration | |
the inertia matrix | |
the Coriolis and centrifugal terms | |
the vector of gravitational force | |
the control input | |
the unknown external disturbance | |
the actuator fault | |
the estimations of q | |
the estimations of y | |
the estimations of w | |
the estimations of E | |
the column vector of output matrix observation errors | |
the estimation of | |
the tracking error vectors | |
the attitude vector of the quadrotor rigid body | |
the estimation errors of q | |
the estimation errors of w |
Parameter | Manipulator 1 | Manipulator 2 | Manipulator 3 | Manipulator 4 |
---|---|---|---|---|
(m) | 0.98 | 1 | 0.96 | 1 |
(m) | 1 | 0.95 | 1 | 1.02 |
(kg) | 1.02 | 0.96 | 1.01 | 1.04 |
(kg) | 1.12 | 1.15 | 1.07 | 1.09 |
(kg · m2) | 0.23 | 0.21 | 0.19 | 0.21 |
(kg · m2) | 0.41 | 0.4 | 0.42 | 0.41 |
The Tracking Errors | Overall Performance and | Overall Performance in [22] and | Steady-State Performance and | Steady-State Performance in [22] and |
---|---|---|---|---|
−0.039, 0.280 | 0.979, 1.475 | −0.006, 0.008 | 1.623, 0.325 | |
0.065, 0.652 | 0.571, 1.760 | −0.003, 0.009 | 1.360, 0.324 | |
0.072, 0.972 | 0.473, 1.708 | −0.006, 0.014 | 1.062, 0.322 | |
−0.011, 1.192 | 0.091, 1.595 | 0.006, 0.014 | 1.322, 0.366 |
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Li, Z.; He, H.; Han, C.; Lin, B.; Shi, M.; Qin, K. The Distributed Adaptive Bipartite Consensus Tracking Control of Networked Euler–Lagrange Systems with an Application to Quadrotor Drone Groups. Drones 2024, 8, 450. https://doi.org/10.3390/drones8090450
Li Z, He H, Han C, Lin B, Shi M, Qin K. The Distributed Adaptive Bipartite Consensus Tracking Control of Networked Euler–Lagrange Systems with an Application to Quadrotor Drone Groups. Drones. 2024; 8(9):450. https://doi.org/10.3390/drones8090450
Chicago/Turabian StyleLi, Zhiqiang, Huiru He, Chenglin Han, Boxian Lin, Mengji Shi, and Kaiyu Qin. 2024. "The Distributed Adaptive Bipartite Consensus Tracking Control of Networked Euler–Lagrange Systems with an Application to Quadrotor Drone Groups" Drones 8, no. 9: 450. https://doi.org/10.3390/drones8090450