Nonsingular Finite Time Adaptive Control for Uncertain Nonlinear Multiagent Systems With Unknown Non-Identical Control Directions

摘要

Under a directed graph, a distributed nonsingular finite time adaptive control algorithm is proposed in this paper for a class of nonlinear multiagent systems (MASs) with parametric uncertainties and completely unknown non-identical control directions. Firstly, a modified coordinate transformation is proposed by introducing the dynamic surface control (DSC) technique, which avoids the massive use of neighbor informations and overcomes the “explosion of complexity” challenge arising from iterative differentiation concerning the virtual controls. Secondly, we adopt a set of Nussbaum functions with different frequencies for each agent to deal with the unknown control directions and make the effects of the multiple Nussbaum functions enhance each other instead of counteracting. In addition, by introducing a piecewise continuous function in each step of the backstepping procedure, a novel nonsingular finite time adaptive tracking controller is designed, which eliminates the possible singularity problems resulting from the presence of negative fractional powers. Based on the finite time stability criterion, it is proved that all closed-loop signals are bounded and the tracking errors can converge to a small residual set in a finite time. Finally, a simulation example of four DC motors is provided to demonstrate the effectiveness of the proposed algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper investigates the distributed nonsingular finite time adaptive consensus tracking control problem for the nonlinear MASs with parametric uncertainties and completely unknown non-identical control directions, whose models can describe many critical applications, such as unmanned vehicle formation and robot formation. The proposed algorithm provides an intuitive design paradigm for the consensus tracking control of uncertain nonlinear MASs with completely unknown non-identical control directions. In addition, the developed finite time control method can effectively increase the system convergence, which makes the designed algorithm more engineering oriented.