Robust Adaptive Control for Nonlinear Multi-Agent Systems: A Physics-Regularized Neural Backstepping Approach

Significant theoretical and practical challenges arise in the cooperative control of distributed nonlinear multi-agent systems (MAS), particularly when they involve nonstrict-feedback interconnections and unknown state-dependent control gains. Conventional neural adaptive controllers, while versatile, often operate as “black-box” models, leading to solutions that may lack physical plausibility and exhibit compromised robustness. This paper addresses this critical gap by introducing a novel Physics-Regularized Adaptive Control (PRAC) framework, implemented via neural backstepping. Central to PRAC is the design of novel Physics-Regularized Neural Networks (PRNNs), which are realized using Radial Basis Function Neural Networks (RBFNNs) as their architectural foundation in this paper. Instead of treating the neural network as a simple approximator, the PRAC methodology embeds physical priors, such as equilibrium conditions, system smoothness, and energy dissipation principles, into the PRNNs’ online adaptive laws as differentiable regularization terms. The gradients of these terms actively constrain the PRNN weight adaptation, transforming the learning process into a Lyapunov-guided constrained optimization. This enhances the physical consistency and interpretability of the learned dynamics while simultaneously improving control performance. By synergistically combining this physics-regularized architecture with Dynamic Surface Control (DSC) to manage computational complexity, the proposed scheme guarantees cooperative uniformly ultimately bounded (CUUB) tracking of a leader’s trajectory. Rigorous Lyapunov analysis substantiates the theoretical guarantees, which are further validated by comprehensive numerical simulations and a practical networked inverted-pendulum example demonstrating superior tracking accuracy and robustness over conventional neural adaptive controllers.