Prescribed-time reinforcement learning formation control of nonlinear MASs with an unknown dynamic leader

Abstract

This paper investigates the prescribed-time optimal formation control problem for nonlinear multi-agent systems (MASs) with an unknown dynamic leader. The agents need to not only form a predefined formation pattern but also track the leader’s trajectory in a prescribed time. A hierarchical control framework, which includes the communication layer and the tracking control layer, is established to address the formulated issue. In the communication layer, a distributed prescribed-time observer is established to accurately estimate the leader’s information, which can make observation error convergences to zero in a prescribed time. In particular, the leaders’ uncertainties are solved by constructing a novel adaptive law. With the estimated results, a novel transformation relationship and the prescribed-time adjustment function are constructed to guarantee that formation tracking error converges to the predefined accuracy in a prescribed time. Subsequently, the reinforcement learning (RL) algorithm with the fuzzy logic systems (FLSs) is devised to optimize system performance. Based on the Lyapunov stability theory, it is shown that the formation errors ${\xi }_{i,1}=x_{i,1}-{\hat{y}}_{0,i}-{\eta }_{i,d}$ are consistently confined within an interval $(\tan (-\frac{\pi }{2{\mu }_2}),\tan \left(\frac{\pi }{2{\mu }_2}\right))$, while all signals of the closed-loop system are bounded. Ultimately, the superiority of the devised algorithm is demonstrated by a representative example.