Investigating Formation and Containment Problem for Nonlinear Multiagent Systems by Interval Type-2 Fuzzy Sliding Mode Tracking Approach

A fuzzy sliding mode (FSM) tracking approach is proposed by interval type-2 (IT-2) Takagi–Sugeno fuzzy model (T-SFM) to complete formation and containment (F-and-C) tasks for nonlinear multiagent systems (NMAS) systems with uncertainties and disturbances. Using an 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 to ensure 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 multiagent (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 multiship system (NMSS) to illustrate the advantage.