Robust Adaptive Fuzzy Fixed-Time Distributed Time-Varying Optimization in Unbalanced Nonlinear Second-Order Multiagent Networks

This paper focuses on the problem of robust adaptive fuzzy fixed-time distributed time-varying optimization (FxT-DTVO) for nonlinear second-order multi-agent systems (SOMASs) with input saturation and unmatched disturbances over unbalanced networks. A fixed-time robust adaptive fuzzy tracking strategy is applied to solve the FxT-DTVO problem. First, a gradient-sum-estimation-based fixed-time distributed optimization reference signal is designed to realize the FxT-DTVO in an unbalanced signal network. Subsequently, a fixed-time disturbance estimation algorithm is designed to estimate the unmatched disturbance. Based on the designed disturbance estimation and reference signal, two hierarchical coordinated tracking errors are defined to transform the SOMASs into error dynamic systems. To realize fixed-time stabilization of the error dynamic systems, a fixed-time robust adaptive fuzzy tracking algorithm based on sliding mode control is established, where the robust adaptive term with composite learning robust adaptive law is estimated online to compensate for the effect of input saturation and the unknown interference term. The unknown and continuous nonlinear part is approximated by a fuzzy logic system. The fixed-time stabilization of the error dynamic system means that the nonlinear SOMASs track the time-varying optimization reference signal within a fixed time, and the studied FxT-DTVO problem is thus solvable. Finally, two examples are employed to verify the correctness and good performance of the designed algorithm.