Distributed Adaptive NN-Based Attitude Synchronous Tracking Control with Input Saturation
Abstract
:1. Introduction
- The proposed distributed attitude coordination controller for SFF is robust against external disturbances and inertia uncertainties with input saturation. The stability of the controller is verified by Lyapunov’s method and the tracking errors are uniformly ultimately bounded (UUB).
- A ChNN-based approximator, which has the advantages of computational simplicity and easy application [31] is implemented in the proposed controller, and in simulation, it is discovered that chattering caused by the switch function can be avoided by applying a filter.
- A Nussbaum-type function is introduced to the ASTC to handle the nonlinearity arising from input saturation. This approach can be easily extended to other control problems.
2. Problem Statement
2.1. Attitude Dynamics of Rigid Spacecraft
2.2. Actuator with Input Saturation
2.3. Control Object
3. Preliminaries and Lemmas
3.1. Graph Theory
3.2. Nussbaum-Type Function
- 1.
- , where γ is a constant;
- 2.
- ;
- 3.
- ;
- 4.
- Suppose that and are invertible, then ;
- 5.
- Let be the eigenvalues of , and be those of . Then the eigenvalues of are .
3.3. The Chebyshev Neural Network
4. Main Results
4.1. Multi-Spacecraft Sliding Manifold Derivation
4.2. Controller Synthesis
4.2.1. Control Law Design
4.2.2. Stability Analysis
5. Simulation Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Symbols | |
adjacency matrix | |
connection matrix | |
external disturbance vector, | |
control torque vector, | |
inertia tensor, | |
nominal inertia tensor, | |
Laplacian matrix | |
S | multi-spacecraft sliding-mode vector |
V | Lyapunov function |
inertia uncertainty, | |
in-degree matrix | |
upper bound on the norm of external disturbance | |
upper bound on the norm of inertia uncertainty | |
minimum eigenvalue of matrix | |
modified Rodriguez parameter vector | |
attitude (MRPs) tracking error | |
commanded control signal, | |
angular velocity, | |
angular velocity tracking error, | |
Euclidean norm | |
vector cross-product matrix | |
⊗ | Kronecker product |
Acronyms | |
NN | neural network |
ChNN | Chebyshev neural network |
SFF | spacecraft formation flying |
ASTC | attitude synchronization and tracking control |
SMC | sliding-mode control |
MRPs | modified Rodriguez parameters |
UUB | uniformly ultimately bounded |
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n | Inertia Matrix | Inertia Uncertainty | External Disturbance |
---|---|---|---|
1 | |||
2 | |||
3 | |||
4 |
Controller | MSTE | MSCT () |
---|---|---|
The proposed controller | 0.0061 | 0.0254 |
The comparison controller | 0.1405 | 0.0427 |
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Feng, Z.; Wang, J.; Wan, N.; Li, H. Distributed Adaptive NN-Based Attitude Synchronous Tracking Control with Input Saturation. Electronics 2022, 11, 4093. https://doi.org/10.3390/electronics11244093
Feng Z, Wang J, Wan N, Li H. Distributed Adaptive NN-Based Attitude Synchronous Tracking Control with Input Saturation. Electronics. 2022; 11(24):4093. https://doi.org/10.3390/electronics11244093
Chicago/Turabian StyleFeng, Zhenyu, Jiawei Wang, Neng Wan, and Huayi Li. 2022. "Distributed Adaptive NN-Based Attitude Synchronous Tracking Control with Input Saturation" Electronics 11, no. 24: 4093. https://doi.org/10.3390/electronics11244093