Error-Constrained Fixed-Time Synchronized Trajectory Tracking Control for Unmanned Airships with Disturbances
Abstract
1. Introduction
- For accurate trajectory tracking, the error should be confined to a specified range, ensuring compliance with practical performance criteria. Through the implementation of the error transformation function (ETF), the tracking errors are systematically transformed, enforcing tracking errors strictly confined in prescribed time-varying error boundaries throughout the tracking process.
- Distinct from conventional nonlinear control approaches that are irrespective of synchronization of each state convergence, built upon the Norm-Normalized sign (NNS) function, this work establishes a control algorithm, effectively ensuring simultaneous stabilization of all tracking error and estimation error components.
- In contrast to DOs that solely ensure fixed-time disturbance estimation, this work proposes a fixed-time synchronized disturbance observer (FTSDO) to achieve the exact reconstruction of uncertain disturbances while guaranteeing the synchronous fixed-time convergence of all estimation errors.
2. Preliminaries
- 1.
- The same constants , and in Lemma 1 satisfy the inequality in (3).
- 2.
- The system state maintains ratio persistence:
3. Problem Statement
3.1. Airship Model
3.2. Model Transformation
3.3. Control Objective
4. Main Results
4.1. Fixed-Time Synchronized Observer Design
4.2. Fixed-Time Synchronized Controller Design
- 1.
- Smooth, monotonically increasing;
- 2.
- ;
- 3.
- , ;
4.3. Stability Analysis
- Based on Theorem 1, , for all , and is arbitrarily small. Therefore, all tracking errors are fixed-time stable according to Lemma 1. Combining (50) with Lemma 3, exhibits FTSS with the convergence time . Then, from (38), we have , and and achieve synchronized stability with the convergence time . Consequently, , all tracking errors exhibit FTSS.
- Furthermore, considering inequality (60), since if and only if , and given the initial condition , we can rigorously establish that the error constraint remains strictly satisfied throughout the convergence process.
5. Simulation
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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FTSS | FT | SM | FTSDO | ||||
---|---|---|---|---|---|---|---|
Parameter | Value | Parameter | Value | Parameter | Value | Parameter | Value |
0.3 | 0.8 | 0.8 | 2 | ||||
0.6 | 0.8 | 0.4 | 2 | ||||
0.3 | 0.5 | 2 | 0.65 | ||||
0.6 | 0.5 | ð | 2 | 1.1 | |||
0.65 | – | – | – | – | 0.05 | ||
0.65 | – | – | – | – | 3 | ||
1.1 | – | – | – | – | – | – | |
1.1 | – | – | – | – | – | – |
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Chen, J.; Yuan, J.; Li, R. Error-Constrained Fixed-Time Synchronized Trajectory Tracking Control for Unmanned Airships with Disturbances. Drones 2025, 9, 403. https://doi.org/10.3390/drones9060403
Chen J, Yuan J, Li R. Error-Constrained Fixed-Time Synchronized Trajectory Tracking Control for Unmanned Airships with Disturbances. Drones. 2025; 9(6):403. https://doi.org/10.3390/drones9060403
Chicago/Turabian StyleChen, Jie, Jiace Yuan, and Ruohan Li. 2025. "Error-Constrained Fixed-Time Synchronized Trajectory Tracking Control for Unmanned Airships with Disturbances" Drones 9, no. 6: 403. https://doi.org/10.3390/drones9060403
APA StyleChen, J., Yuan, J., & Li, R. (2025). Error-Constrained Fixed-Time Synchronized Trajectory Tracking Control for Unmanned Airships with Disturbances. Drones, 9(6), 403. https://doi.org/10.3390/drones9060403