Cooperative Deterministic Learning-Based Formation Control for a Group of Nonlinear Mechanical Systems Under Complete Uncertainty

TL;DR

The paper tackles distributed formation control for a group of nonlinear mechanical systems with complete uncertainty under a virtual leader-following framework. It introduces a two-layer scheme: an upper-layer cooperative nonlinear estimator to recover the leader's state and a lower-layer cooperative deterministic learning controller that uses Radial Basis Function Neural Networks to approximate the uncertain dynamics $G(x)$ and achieve formation tracking with online weight consensus. The authors prove stability results including Uniform Ultimate Boundedness (UUB) and exponential convergence of tracking errors, along with convergence of NN weights toward a common optimal value, enabling cooperative learning across the network. Numerical simulations with four agents validate precise tracking, robust formation maintenance, and knowledge consensus, demonstrating practical applicability for robust distributed formation control under complete uncertainty.

Abstract

In this work we address the formation control problem for a group of nonlinear mechanical systems with complete uncertain dynamics under a virtual leader-following framework. We propose a novel cooperative deterministic learning-based adaptive formation control algorithm. This algorithm is designed by utilizing artificial neural networks to simultaneously achieve formation tracking control and locally-accurate identification/learning of the nonlinear uncertain dynamics of the considered group of mechanical systems. To demonstrate the practicality and verify the effectiveness of the proposed results, numerical simulations have been conducted.

Figures (6)

• Figure 1: Network topology and desired formation pattern.
• Figure 2: Cooperative nonlinear estimation.
• Figure 3: Position tracking responses.
• Figure 4: Function approximation of $G_k(x_1)$ using $\bar{W}_{k,1}^{T} S_k(x_1)$.
• Figure 5: MAS formation control.