Secure Distributed Adaptive Control of Nonlinear Multi-Agent Systems

This paper addresses the problem of secure consensus tracking control for nonlinear leader-follower multi-agent systems, with a specific focus on safeguarding followers' private information from external network eavesdroppers or internal untrusted neighbors. To tackle this problem, we first employ the dynamic linearization approximation technique to transform the nonlinear system models into equivalent linear forms that involve unknown time-varying pseudopartial derivatives. Then, a novel model-free secure distributed adaptive control (MFSDAC) framework is proposed using an encoding-decoding mechanism and Paillier encryption. Within this framework, we develop a secure distributed control scheme using a recursive form and design an adaptive updating law with a modified projection to estimate the time-varying pseudoparial derivatives. To enhance security, we introduce an adjustable parameter and a random integer into the distributed communication protocol, effectively preventing the disclosure of followers' data during both network transmissions and controller evaluations. Additionally, parameter selection rules for the controller, quantizer, and adaptive updating law are provided, along with convergence analysis and guarantees against quantizer saturation. Finally, numerical simulations confirm that the proposed MFSDAC framework successfully achieves leader-following tracking and secure data transmission, even in the presence of external network eavesdroppers or internal untrusted neighbors. Note to Practitioners-Multi-agent systems (MASs) provide a versatile framework for modeling and understanding various real-world applications, including autonomous systems, traffic management, and distributed sensor networks. Designing effective control strategies for MASs is essential to enhance cooperation and coordination among agents, strengthen system-level resilience and adaptability, and tackle complex tasks that surpass the capabilities of individual agents. A key challenge in this area is ensuring network security and protecting individual privacy, especially in the presence of external eavesdroppers and untrusted internal neighbors. To tackle this challenge, we propose a model-free secure distributed adaptive control framework for nonlinear leader-follower MASs. This framework incorporates a confidential communication protocol that leverages homomorphic encryption to protect sensitive information. The proposed framework has undergone rigorous stability analysis and been validated through numerical simulations, demonstrating its feasibility and effectiveness in achieving secure consensus control of nonlinear MASs.