Predefined-Time Neural Adaptive Control for Distributed Formation Control of Nonlinear Multiagent Systems with Full-State Constraints

This paper investigates the distributed formation control problem for nonlinear multiagent systems subject to full-state constraints and proposes a predefined-time neural adaptive control scheme based on a nonlinear mapping technique. To handle the time-varying asymmetric constraints on system states, a smooth and invertible nonlinear mapping function is introduced to transform the original constrained states into unconstrained variables, thereby eliminating the dependence on initial conditions typically required by traditional barrier Lyapunov functions. Within this transformed framework, a predefined-time distributed formation control law is developed, which guarantees that all followers converge to the desired formation configuration and track the leader’s trajectory within a user-specified time upper bound, independent of the initial states. Radial basis function neural networks are employed to approximate the unknown nonlinear dynamics of each agent, and adaptive laws are designed to update the network weights online. Theoretical analysis shows that all closed-loop signals remain bounded, the original system states strictly stay within their prescribed constraint boundaries at all times, and the formation tracking errors converge to a small neighborhood of the origin within the predefined time. Numerical simulations validate the effectiveness of the proposed method, demonstrating faster convergence, higher steady-state accuracy, and improved robustness to initial conditions compared to existing control approaches.