Adaptive fuzzy singularity-free finite-time optimal control for nonlinear pure-feedback multiagent systems

Abstract

In this paper, we investigate the adaptive fuzzy singularity-free finite-time optimal consensus problem for nonlinear pure-feedback multiagent systems (MASs). For purpose of achieving the optimized control, the fuzzy approximation-based reinforcement learning is employed under critic-actor architecture. By virtue of Butterworth low-pass filter, a distributed adaptive finite-time optimal consensus method is developed for nonlinear pure-feedback MASs, which solves algebraic loop problem produced in the construction of the optimal controller. Most importantly, to be free of singularity, we design a new dynamic filtering optimized backstepping method to avoid the differentiations of virtual optimal controllers, and the errors between first-order filter signals and virtual optimal controllers can be counteracted by designing the smooth robust compensators for the first time. It is shown that, with the developed adaptive finite-time optimal consensus control, both the optimal consensus tracking performance and finite-time convergence for the closed-loop systems are ensured. Three simulation examples are presented to verify the effectiveness of the proposed approach.