Asymptotic Leader-Following Consensus of Heterogeneous Multi-Agent Systems with Unknown and Time-Varying Control Gains

This paper investigates the consensus tracking control problem for a class of nonlinear multi-input multi-output (MIMO) heterogeneous multi-agent systems (HMASs), where the dimension of the dynamics of each agent is allowed to be different from each other. In addition, the control gain matrices (CGMs) with unknown time-varying coefficients and actuator faults with unpredictable jumps are also involved in the considered MIMO HMASs, all of which would cause damage for the system performance. First, a novel distributed auxiliary filter by feat of time-varying technology is introduced, which allows the zero-error estimation for the desired trajectory to be achieved and the asymptotic consensus tracking result to be further realized. Then, a cooperative adaptive control solution is proposed to ensure the asymptotical consensus tracking control result, in spite of the inherent unknown time-varying coefficients, unpredictable jumps caused by the unknown actuator faults, unknown disturbances and uncertain system parameters, distinguishing itself from those existing cooperative control works for HMASs where only ultimately uniformly bounded (UUB) result is derived. This is achieved mainly by the introduction of a series of Nussbaum functions and the employment of the adaptive estimation techniques. The effectiveness of the proposed control algorithm is confirmed by the simulation conducted on a group of HMASs involving unmanned aerial vehicles (UAVs) and autonomous surface vessels (ASVs). Note to Practitioners - In large-scale complex communication networks, uncertain HMASs with different structures and functions are capable of exchanging information and collaborating with each other to accomplish more complex and diverse tasks. Simultaneously, the probability of actuator faults within the HMASs increases dramatically, and the fault of a single agent may evolve into the failure of the whole system. Thus, the safety and reliability of HMASs are extremely important. Additionally, the control direction (the symbol of control gain) caused by both CGMs with coupling property of MIMO systems and actuator faults with unpredictable jumps, may not be guaranteed to be known in practical application, such as ship autopilot systems or uncalibrated visual servoing. This will have a considerable influence on the system's control performance. On account of the threat of nonlinear uncertainties, and unknown control direction yield CGMs and actuator faults to HMASs, an adaptive fault-tolerant control solution based on an effective distributed time-varying auxiliary filter, is developed for MIMO HMASs to guarantee the asymptotical consensus tracking control result. Further, the proposed control scheme has been illustrated to be feasible through simulation experiment conducted on a group of HMASs consisting of UAVs and ASVs.