Practical finite-time and fixed-time containment for second-order nonlinear multi-agent systems with IDAs and Markov switching topology

In this article, the finite-time containment problem and the fixed-time containment problem accompanied by injection and deception attacks (IDAs) and Markov switching topology for second-order nonlinear multi-agent systems (MASs) are investigated, respectively. By introducing a radial basis function neural network (RBFNN), the approximation property of radial basis neural networks is used to solve the unmeasurable difficulties of nonlinear functions and injection attacks. Finite-time and fixed-time distributed control protocols are proposed for switching topologies and attack-induced state deception and control injection, and finite-time and fixed-time containment as well as obtaining their corresponding sufficient conditions are achieved, respectively. Correspondingly, two examples are shown to demonstrate the feasibility of the control protocols.