Hyperchaotic Privacy-Preserving Cooperative Adaptive Control With Application to Multimotor Systems

This article investigates the privacy-preserving cooperative adaptive control problem for nonlinear multiagent systems with unknown disturbances. First, by leveraging the hyperchaotic phenomenon of the Lorenz–Stenflo system, a masking function is proposed, which endows it with uncertainty and unpredictability and thus greatly improves the encryption performance. Meanwhile, a time-assist function is designed to achieve privacy protection within a preassigned period, which enhances the flexibility of the mechanism. In addition, according to the gradient descent method, a dynamically self-adjustable gain parameter is designed in the disturbance observer. The utilization of this parameter enables the proposed observer not only to handle unknown disturbances, but also to better improve the performance of the system. Afterward, the Lyapunov stability theorem is utilized to prove that all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, experimental results validate the effectiveness of the proposed algorithm, which successfully accomplishes speed synchronization across multiple permanent magnet synchronous motors, thereby ensuring secure data transmission.