DR-TVFC

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DR-TVFC is a control framework based on sliding mode control that decouples the consensus task and the formation task to achieve distributed formation tracking control for multi-agent control systems (MAS).

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## DR-TVFC(Distributed Robust Time-Varying Formation Control) of MASs under Disturbances

by **Guang-Ze Yang $^1$** and **Zi-Jiang Yang $^2$**

> **Abstract:** This work considers the problem of time-varying formation tracking control of second-order multi-agent systems under disturbances. The DR-TVFC(distributed robust time-varying formation control) is proposed including **distributed finite-time estimators of the leader’s states** and **sliding mode time-varying formation controllers**. Firstly, each agent can quickly estimate the leader’s states through the communication network in the distributed finite-time estimators based on the sliding mode estimation. Secondly, utilizing the estimates of the leader’s states, a sliding mode time-varying formation controller is designed using **the prescribed time modification function**. Unlike traditional distributed control law relying on the exchanges of the agents’ states, the proposed control design achieves great robustness and stability of the overall system by **exchanging the estimates of the leader’s states**. According to Lyapunov stability analysis, we prove that the proposed approach enables the sliding variables to achieve fast finite-time convergence. Furthermore, simulation examples are provided to illustrate the performance.

This work has been accepted by 2024 63rd Annual Conference of SICE.

**G. -Z. Yang** and Z. -J. Yang, "Distributed Robust Time-Varying Formation Control of Multi-Agent Systems Under Disturbances," 2024 SICE Festival with Annual Conference (SICE FES), Kochi City, Japan, 2024, pp. 1000-1005. [[IEEE Xplore]](https://ieeexplore.ieee.org/document/10805135) [[Code]](https://github.com/youkoutaku/DR-TVFC)

### Description

![](https://raw.githubusercontent.com/youkoutaku/DR-TVFC/main/Image/Framework.png)

![](https://raw.githubusercontent.com/youkoutaku/DR-TVFC/main/Image/Conclusion.png)

## Program Description
### `config.m`
- System Parameters and control parameters.
### `Leader_state.m`
- generate reference signal (Trajectory) and Plot the fig.
### `Formation_shape.m`
- generate time-varying formation shape and Plot the fig.
### `main.m`
- Estimator.
- Prescribed time modification.
- Sliding mode formation controller.
- System simulation.
### Figure programs in `Plot`
- Main figure
   1. `fig_motion.m`: 3D plotting of the agents' movement.
   2. `fig_error_e.m`: The errors of the estimator.
   3. `fig_states.m`: The states of the agents.
   4. `fig_error_pro.m`: The errors fo the formation controller.
   5. `fig_input.m`: The input of the formation controller.
   6. `Animation.m`: The animation of the agents' movement. (Run after finished `fig_states.m`)
- Addition figures
   1. `fig_states_e.m`: The states of the estimator.
   2. `fig_vinput.m`: The virtual input of the estimator.
   3. `fig_em.m`: The modified formation tracking errors.
   4. `fig_xi.m`: The prescribed time modification function.
   5. `fig_sliding.m`: The sliding variable.

## Running

```matlab
build.m
```

![](https://raw.githubusercontent.com/youkoutaku/DR-TVFC/main/Image/3D.png)

![](https://raw.githubusercontent.com/youkoutaku/DR-TVFC/main/Image/Animation.gif)

## Citation
If you use the code in your research, please consider citing:
```
@INPROCEEDINGS{10805135,
  author={Yang, Guang-Ze and Yang, Zi-Jiang},
  booktitle={2024 SICE Festival with Annual Conference (SICE FES)}, 
  title={Distributed Robust Time-Varying Formation Control of Multi-Agent Systems Under Disturbances}, 
  year={2024},
  pages={1000-1005},
```

1. Department of Mechanical Systems Engineering, Ibaraki University, Hitachi, Japan; Tel: +81-294-38-5205; E-mail: 24nm499s@vc.ibaraki.ac.jp
2. Department of Mechanical Systems Engineering, Ibaraki University, Hitachi, Japan;Tel: +81-294-38-5205; E-mail: shikoh.yoh.zijiang@vc.ibaraki.ac.jp

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