Adaptive Fault-Tolerant Consensus Tracking Control for Nonlinear Multi-Agent Systems with Double Semi-Markovian Switching Topologies and Unknown Control Directions

This paper is concerned with adaptive consensus tracking control of nonlinear multi-agent systems with actuator faults and unknown nonidentical control directions under double semi-Markovian switching topologies. Considering the complex working environment and the stability differences in communication links between leaders and followers, a double semi-Markov process is first introduced to describe the random switching of communication topologies in the leader-follower structure. In order to address challenges from the unknown nonidentical control directions and partial loss of effectiveness actuator faults, a completely independent parameter is introduced into the Nussbaum function to overcome the inherent obstacle of mutual cancellation and avoid the rapid growth rate. Considering only the state information of agents is transmitted among the agents, an adaptive distributed fault-tolerant consensus tracking control is proposed based on the double semi-Markovian switching topologies using the designed Nussbaum function. Furthermore, the stability of the closed-loop nonlinear multi-agent systems is analyzed using contradiction argument and Lyapunov theorem, from which the asymptotic consensus tracking in mean square sense can be obtained. A numerical simulation example is provided to verify the effectiveness of the proposed algorithm.