Distributed Adaptive Neural Control of Unknown Stochastic Nonlinear Multi-Agent Systems With Time-Varying Delays and Unknown Control Directions

Abstract

Multi-agent systems (MASs) are widely applied in complex, uncertain environments. Yet, their distributed control faces significant challenges due to unknown agent nonlinearities, stochastic disturbances, time-varying (TV) communication delays, and unknown control directions (UCDs). Designing robust and efficient control strategies for such complex systems, especially high-order strict-feedback stochastic MASs, remains a critical, unresolved problem in control theory. This paper introduces a novel distributed adaptive neural control approach for strict-feedback stochastic MASs with TV delays and UCDs under switching directed topologies. Radial basis function neural networks (RBFNNs) are used to approximate uncertain nonlinear functions, while a Nussbaum-type function eliminates the need for prior knowledge of the signs of the control gains. To overcome the “explosion of complexity” common in backstepping, a dynamic surface control (DSC) framework with command filters and minimal learning parameters (MLP) is employed, significantly reducing computational overhead. Adaptive laws based on Lyapunov-Krasovskii functionals are constructed to handle unknown state delays without requiring knowledge of their bounds or derivatives. It is rigorously proven that all signals in the closed-loop are cooperatively semi-globally uniformly ultimately bounded (CSGUUB) in probability, and tracking errors converge to a tunable neighborhood of the origin. Simulation results on a MAS with unknown stochastic nonlinearities, TV delays, and UCDs confirm the effectiveness and robustness of the proposed method. Note to Practitioners—Many engineered systems today rely on cooperation among multiple units rather than centralized control. Examples include fleets of autonomous vehicles, teams of mobile robots, distributed energy resources, and large-scale industrial processes connected through communication networks. In such systems, accurate mathematical models are rarely available, communication delays vary over time, external disturbances are unavoidable, and actuator behavior may be uncertain or poorly characterized. These practical issues often prevent existing distributed control methods from being deployed outside laboratory settings. The control strategy presented in this paper is intended for situations where model information is incomplete and operating conditions change over time. The proposed method adapts online to unknown nonlinear behaviors and random disturbances without requiring prior identification or tuning based on detailed system models. It also tolerates unknown communication delays and does not assume knowledge of the direction of control effectiveness, which is particularly relevant when actuators age, are replaced, or behave differently across agents. From an implementation standpoint, the controller relies only on local information exchanged between neighboring agents and avoids computationally intensive structures, making it suitable for systems with limited onboard resources. The main benefit of the proposed approach is robustness rather than optimality. While it guarantees bounded tracking performance under uncertainty, it does not enforce strict optimal control or perfect convergence, and transient control signals may be larger when a faster response is required. Practitioners may therefore view this method as a reliable baseline solution for uncertain, safety-critical multi-agent applications, which can be extended or combined with optimization, constraint handling, or event-triggered mechanisms to meet specific industrial requirements.