Resilient Formation Control With Koopman Operator for Networked NMRs Under Denial-of-Service Attacks

This article presents a resilient formation control framework for networked nonholonomic mobile robots (NMRs) that enables long-time recovery abilities subject to denial-of-service (DoS) attacks by taking advantage of the Koopman operator. Due to the intermittent interruption of communication under DoS, the transmitted signals among the networked NMRs are incomplete. In the lifted space, the infinite-dimensional Koopman operator is employed to capture a linear characteristic of the missed signals from the available signals. Specifically, a data-driven cost function is developed to approximate the infinite-dimensional Koopman operator, allowing long-term recovery capabilities for the missed signals, where the useful historical data is identified by an event-triggered mechanism (ETM). Then, the least-squares method is implemented to calculate a finite-dimensional approximation of the Koopman operator. Once DoS attacks are active, the missed signals are recovered forward from the latest received signals through the approximation Koopman operator. Furthermore, according to the recovered and transmitted signals, the resilient formation controller with a variable gain takes into account the convergence rate and the steady state formation error. The Lyapunov theorem is introduced to prove that the formation error quickly converges to the minor compact set. A distributed DoS attack example is conducted to validate the efficiency and superiority in numerical simulation, and the proposed method is implemented on the real networked NMRs.