Adaptive Robust Tracking Control for Multiple Unknown Fractional-Order Nonlinear Systems
针对具有未知非线性、外部干扰和未知有界领导者输入的分数阶多智能体系统，设计了基于神经网络的全分布式鲁棒自适应算法，实现跟踪误差指数收敛或一致最终有界。
By applying the fractional Lyapunov direct method, we investigate the robust consensus tracking problem for a class of uncertain fractional-order multiagent systems with a leader whose input is unknown and bounded. More specifically, multiple fractional-order systems with heterogeneous unknown nonlinearities and external disturbances are considered in this paper, which include the second-order multiagent systems as its special cases. First, a discontinuous neural network-based (NN-based) distributed robust adaptive algorithm is designed to guarantee the consensus tracking error exponentially converges to zero under a fixed topology. Also the derived results are further extended to the case of switching topology by appropriately choosing multiple Lyapunov functions. Second, a continuous NN-based distributed robust adaptive algorithm is further proposed to eliminate the undesirable chattering phenomenon of the discontinuous controller, where the consensus tacking error is uniformly ultimately bounded and can be reduced as small as desired. It is worth noting that all the proposed NN-based robust adaptive algorithms are independent of any global information and thus are fully distributed. Finally, numerical simulations are provided to validate the correctness of the proposed algorithms.