Optimal Formation Control of Second-Order Heterogeneous Multiagent Systems Using Adaptive Predefined-Time Strategy
Jiaxin Zhang, Yue Fu, Jun Fu
Abstract
This article proposes a novel predefined-time optimal formation control approach for second-order heterogeneous multiagent systems with nonlinear dynamics and external disturbances. Fuzzy logic systems are used to identify unknown nonlinearities. To enhance the system's robustness against external disturbances, an <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 strategy is implemented. The predefined-time optimal formation control method is developed by leveraging backstepping technology and actor–critic framework. This approach is designed to guarantee that the closed-loop system is practical predefined-time stable and <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 or equal to a positive real number <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\nu$</tex-math></inline-formula> , and all system signals are predefined-time bounded while minimizing the cost of maintaining a formation pattern between the leader and followers. Simulation results validate the effectiveness and superiority of this control strategy.