Initial-Value-Free Nonlinear Mapping-Based Approach to Practical Finite/Fixed-Time Consensus Control for Constrained Multiagent Systems

This article explores the practical finite/fixed-time consensus control algorithms for nonlinear multiagent systems (MASs) using an initial-value-free nonlinear mapping (NM) approach. By integrating a piecewise continuous function into each virtual control, the novel control signal can effectively avoid the singularity problem inherent in finite-time and fixed-time work. Compared with the previous constrained papers, we reconstruct the nonlinear MASs by introducing boundary performance functions into the NM method to release the initial-value conditions. Then, a command-filtered technique is provided to tackle the issue of the “explosion of complexity” stemming from iterative differentiation regarding the virtual controls, while a twice-transformation design technique is used to compensate for the filtered error. The adaptive controllers utilizing radial basis function neural networks (RBF NNs) can effectively address the effects of the unknown control gains and system uncertainties. The explored control strategies ensure that all signals of the closed-loop system converge into a compact set near zero within a practical finite/fixed time without violating the imposed constraints. Ultimately, the simulation outcomes on robotic systems illustrate the availability of the designed algorithms.

I. Introduction

Consensus control has been addressed in-depth for multiagent systems (MASs) in engineering practice, which has tremendously generated the relevant explorations on various scenarios [1], [2], [3], [4], [5], [6], [7], such as the formation flying problem, multirobot systems, physical and biological systems, and others. Moreover, compared with the uniform ultimate bounded results for MASs [8], [9], [10], [11], [12], [13], a greater focus has been directed toward the finite/fixed-time control due to its practicality. For example, Niu et al. [11] studied an adaptive switched control scheme for a single-link manipulator, leading the trajectory tracking error to approach zero. Additionally, Liu et al. [10] explored the fixed-time consensus issue for the double-integrator agents under the influence of uncertain disturbances by using a team-triggered mechanism. However, the singularity problem and “explosion of complexity” problem still occur in these studies.