Predictor-based state-constrained bipartite formation control for nonlinear multi-agent systems with disturbances

Constrained states and transient performance are critical in bipartite formation control of multi-agent systems. In this paper, a predictor-based state-constrained bipartite formation control strategy is proposed for a class of nonlinear multi-agent systems with unknown external disturbances. A dual barrier Lyapunov function is proposed to constrain both prediction errors and predictor-based surface errors. With the help of the dual barrier Lyapunov function, a barrier Lyapunov function-based predictor is then constructed. It alleviates oscillations generated by overlarge adaptive gains in identification of state-constrained followers. With a barrier Lyapunov function-based predictor, barrier Lyapunov function neural networks are developed to approximate unknown dynamics of a multi-agent system with state constraints. A barrier Lyapunov function neural network nonlinear disturbance observer is designed for compensating for generalized disturbances including disturbances as well as barrier Lyapunov function neural networks’ identification errors. From analysis, it is proven that the multi-agent system achieves bipartite formation and states of followers satisfy the constrained condition. The effectiveness of the strategy with state constraints is verified via two simulation examples. Compared with the traditional approaches, the proposed strategy reduces the integrated absolute formation error by 31% and the integrated absolute error of identification by 63% during the simulation process.