Adaptive Fixed-Time Safety Concurrent Control of Vehicular Platoons with Time-Varying Actuator Faults under Distance Constraints
Abstract
:1. Introduction
- (1)
- A new Nussbaum function with smaller amplitudes is designed, with which the unknown time-varying actuator fault directions are dealt with, without depending on the precise boundary values for the efficiency loss factor.
- (2)
- A unified BLF method based on the bias constraint function is proposed, which can transform the asymmetric constraint into a symmetric one, making the control design simpler.
- (3)
- Together with the proposed Nussbaum function and BLF method, an adaptive fixed-time sliding mode control scheme is developed for a third-order platoon system, with which the individual vehicle stability and string stability can all be guaranteed within a settling time.
2. Preliminaries and Problem Formulation
2.1. Preliminaries
2.2. Vehicle Dynamics
2.3. Distance Constraints
- Then, the error constraints become
2.4. Control Objectives
- (1)
- Fixed-time individual vehicle stability: A desired inter-vehicle distance can be maintained in a given time (i.e., and when ).
- (2)
- Fixed-time string stability: After a given time , the inter-vehicle spacing tracking error does not increase along the platoon, that is
3. Fixed-Time Sliding Mode Surface and Nussbaum Function
3.1. Sliding Mode Surface Design
3.2. Nussbaum Function
4. Controller Design and Stability Analysis
4.1. Controller Design
4.2. Stability Analysis
5. Simulation Studies
5.1. The Results of the Proposed Control Scheme without Actuator Faults
5.2. The Effect of Unknown Actuator Fault Directions
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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The vehicle’s mass | The external disturbances | ||
The air density | The drag coefficient | ||
The frontal cross-area | The control input | ||
The engine time constant | The engine/brake input |
i | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
(kg) | 1550 | 1450 | 1520 | 1510 | 1390 |
(s) | 0.15 | 0.25 | 0.32 | 0.41 | 0.35 |
(kg/m3) | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 |
(m2) | 2.2 | 2.2 | 2.2 | 2.2 | 2.2 |
0.414 | 0.414 | 0.414 | 0.414 | 0.414 | |
(N) | 236.2 | 236.2 | 236.2 | 236.2 | 236.2 |
(m) | 4 | 4 | 4 | 4 | 4 |
0.1 | 0.1 | 0.1 | 800 | 5000 | 0.9 | 3/7 | 5/3 | 0.2 |
5 | 0.001 | 2 | 0.01 | 10 | 1 | 10 | 0.0001 | 0.0001 |
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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
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Liu, W.; Wei, Z.; Liu, Y.; Gao, Z. Adaptive Fixed-Time Safety Concurrent Control of Vehicular Platoons with Time-Varying Actuator Faults under Distance Constraints. Mathematics 2024, 12, 2560. https://doi.org/10.3390/math12162560
Liu W, Wei Z, Liu Y, Gao Z. Adaptive Fixed-Time Safety Concurrent Control of Vehicular Platoons with Time-Varying Actuator Faults under Distance Constraints. Mathematics. 2024; 12(16):2560. https://doi.org/10.3390/math12162560
Chicago/Turabian StyleLiu, Wei, Zhongyang Wei, Yuchen Liu, and Zhenyu Gao. 2024. "Adaptive Fixed-Time Safety Concurrent Control of Vehicular Platoons with Time-Varying Actuator Faults under Distance Constraints" Mathematics 12, no. 16: 2560. https://doi.org/10.3390/math12162560