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.

Description

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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

build.m

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Update

2024-08-01

The Animation.m program has been modified to make it easier to present.

2024-06-25

Globalize the state of the agents to use matrix computation instead of loops.

2023-03-11

Collision avoidance for MAS. (To be continued)

2024-01-21

The time-varying formation shape is realized using the SMFC algorithm.

2023-11-26

The distributed state estimation for consensus tracking control is introduced to estimate the leader’s states.

2023-11-06

Trying to introduced the NN for disturbances. (Unsuccess)

2023-09-08

The prescribed time modification function to formation tracking errors in SMFC.

2023-07-30

Sliding mode formation controller(SMFC) for Centralized leader-follower is introduced.

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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