Investigating Formation and Containment Problem for Nonlinear Multi-Agent Systems via Interval Type-2 Fuzzy Sliding Mode Tracking Approach

Abstract

A Fuzzy Sliding Mode (FSM) tracking approach is proposed via Interval Type-2 (IT-2) Takagi-Sugeno Fuzzy Model (T-SFM) to complete Formation and Containment (F-and-C) tasks for Nonlinear Multi-Agent Systems (NMASs) with uncertainties and disturbances. Using Imperfect Premise Matching (IPM) approach, the IT-2 F-and-C Fuzzy Controllers (FCs) are designed in accordance with the IT-2 T-SFM. Different from the existing research, the individual tracking FC for each leader is proposed to complete the formation tasks and assignment of whole system dynamics. The stability analysis process is also simplified for ensuring the formation purpose. Benefiting from the advantage, the FSM control is conveniently combined into the FC design to upgrade the performance of leaders. For followers, the analysis methods of linear Multi-Agent (M-A) systems are extended to solve the containment analysis problem without the additional assumption by virtue of the IT-2 T-SFM representation. To deal with the disturbance effect, the passive constraints are combined into the analysis process. Finally, the proposed F-and-C FCs design method is applied to a Nonlinear Multi-Ships System (NMSS) to illustrate the advantage.