Nussbaum-Based Distributed Containment Control for Nonlinear Multiagent Systems With Quantized Inputs

Abstract

This article explores the distributed containment control problem for uncertain nonlinear multiagent systems subject to external disturbances and input quantization, where the constant control gains and the upper bounds of the external disturbances are unknown. First, the reference generator is constructed for each follower agent to generate the virtual tracking signal, confining to the convex hull spanned by the leaders. Meanwhile, the unmeasurable state variable of each follower is estimated by adopting the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula>-filters based on the available output/input signals and known system function matrices. Then, a distributed adaptive output feedback controller with only one updating parameter is designed for each follower by introducing a logarithmic quantization to quantize the control inputs under the framework of prescribed performance control. The lack of a priori knowledge for the control gain and the quantization gain is counteracted effectively by employing the Nussbaum function method in the adaptive backstepping design process. It is proved that the outputs of followers can enter into the convex hull of multiple leaders and the relevant tracking errors satisfy the prescribed performance index. Finally, the validity of the proposed schemes is illustrated through simulation studies on robotic systems.