Funnel-Based Adaptive Predefined-Time Leader-Following Output-Feedback Optimal Control for Second-Order Nonlinear Multi-Agent Systems
Jiaxin Zhang, Yue Fu, Jun Fu
Abstract
This study proposes a novel adaptive funnel-based approach for optimal formation control in second-order nonlinear multi-agent systems (MASs). The nonlinear system considered includes unknown dynamics, with only one measurable output variable. The states, not directly measurable, are reconstructed using fuzzy state observers. In the context of an actor-critic framework, a novel funnel optimal predefined-time formation controller is developed. The primary objective is to achieve practical predefined-time stability in the closed-loop system, confining formation errors within a specified funnel while minimizing the cost of maintaining formation patterns between the leader and followers. Comparative simulations further confirm the advantages of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Cooperative control of multi-agent systems (MASs) has garnered considerable interest in diverse applications, including multi-motor synchronization and spacecraft formation flying. Managing complex engineering systems is challenging with a solitary component, prompting a focus on MASs. Formation control, a key aspect of MASs, has become a prominent research area. In practical applications, certain states are challenging to measure, and performance behaviors, such as convergence rate, maximum overshoot, and maximum steady-state error, often require predefined specifications. Simultaneously, achieving control tasks must be balanced with minimizing resource consumption. This study explores funnel-based output-feedback optimal leader-following control for MASs, emphasizing predefined-time convergence.