Predefined-Time <i>H</i> _∞ Cooperative Control for Multi-Robot Systems Based on Adjustable Prescribed Performance Control and Adaptive Command Filter

Abstract

A predefined-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty } $ </tex-math></inline-formula> coordinated formation controller with an adjustable prescribed performance function (PPF) and an adaptive command filter is proposed for multi-robot systems in this work. First, an adjustable prescribed performance function is developed to limit the angular error and adaptively adjust the state convergence performance subject to actuator saturation, which effectively avoids the singularity problem. Second, the “explosion of complexity” issue is solved by proposing a predefined-time adaptive command filter and accelerate the convergence time and improve filter precision. Third, the predefined-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty } $ </tex-math></inline-formula> control theory is developed to guarantee that the nonlinear system has global predefined-time stabilization and that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> gain is less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula>. Fourth, the predefined-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty } $ </tex-math></inline-formula> coordinated formation controller for multi-robot systems (MRSs) is designed to achieve strong robustness to various disturbances. Finally, all the signals in the control system are bounded and converge within the predefined time, and the results of the virtual simulation experiments verify the validity and performance of the MRSs.