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.

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

An interval type-2 (IT-2) fuzzy control design method is developed to solve the formation and containment problem of nonlinear multi-boiler systems. In most practical industrial systems such as airplanes, vessels, and power plants, the boiler system often exists as more than one piece of equipment. An efficient control theory based on the leader-following multi-agent system is applied to achieve the control purpose of multiple boiler systems simultaneously. Moreover, a faithful mathematical model of the nonlinear boiler system is extended to construct the multi-boiler system so that the dynamic behaviors can be accurately presented. For the control of practical multi-agent systems, the uncertainties problem, which will deteriorate the performance of the whole system greatly, must be considered. Because of this, the IT-2 Takagi–Sugeno (T–S) fuzzy model is developed to represent the nonlinear multi-boiler system with uncertainties more completely. Based on the fuzzy model, the IT-2 fuzzy formation and containment controllers are designed with the imperfect premise matching scheme. Thus, the IT-2 fuzzy control method design can be more flexible for the nonlinear multi-boiler system. Solving the formation problem, a control method without the communication between leaders differs from the previous research. Since leaders achieve the formation objective, the followers can be forced into the specific range formed by leaders. Via the IT-2 fuzzy control method in this paper, not only can the more flexible process of the controller design method be developed to solve the uncertainties problem magnificently, but a more cost-effective control purpose can also be achieved via applying the lower rules of fuzzy controllers. Finally, the simulation results of controlling a nonlinear multi-boiler system with four agents are presented to demonstrate the effectiveness of the proposed IT-2 fuzzy formation and containment control method.

In this paper, a robust fuzzy controller for stochastic nonlinear systems subject to multiple performance constraints is discussed. To solve the problem of stochastic behaviors in nonlinear systems, the covariance control theory and passive control theory are applied based on the concept of energy. Additionally, the pole placement method is considered for the better transient behaviors of the system responses. However, it is known that the control inputs and maximum overshoot of the system responses may become bigger at the same time when the settling time or converge rate of the system is required to be faster. Due to this reason, the input constraint is also considered in the fuzzy controller design method to limit the value of the control gain. Moreover, an effective robust control method is applied to deal with the perturbation of the nonlinear systems. Based on the above performance constraints, the sufficient conditions can be obtained to achieve the stability in the sense of mean square and the multi-performance requirements. Finally, simulation results of the nonlinear synchronous generator system are presented to verify the feasibility and efficiency of the proposed control method.