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

Practical finite-time and fixed-time multigroup consensus questions for second-order nonlinear multi-agent systems (MASs) with Markov switching topologies are investigated in this article. Based on the topology of switching, each agent will appear to switch between different groups, and by setting up group switching signal variables embedded in error variables for each agent, finite-time and fixed-time control protocols are proposed, respectively, such that the conditions that must be satisfied for all agents to achieve practical finite-time multigroup consensus and practical fixed-time multigroup consensus can be obtained, respectively. For unknown nonlinear functions in the dynamical system, a radial basis function neural network (RBFNN) fit is used for approximation. Correspondingly, two examples are provided to verify the control effects of the control protocols.