Computational Design of Interval Type-2 Fuzzy Control for Formation and Containment of Multi-Agent Systems with Collision Avoidance Capability

Abstract

An Interval Type-2 (IT-2) fuzzy controller design approach is proposed in this research to simultaneously achieve multiple control objectives in Nonlinear Multi-Agent Systems (NMASs), including formation, containment, and collision avoidance. However, inherent nonlinearities and uncertainties present in practical control systems contribute to the challenge of achieving precise control performance. Based on the IT-2 Takagi-Sugeno Fuzzy Model (T-SFM), the fuzzy control approach can offer a more effective solution for NMASs facing uncertainties. Unlike existing control methods for NMASs, the Formation and Containment (F-and-C) control problem with collision avoidance capability under uncertainties based on the IT-2 T-SFM is discussed for the first time. Moreover, an IT-2 fuzzy tracking control approach is proposed to solve the formation task for leaders in NMASs without requiring communication. This control scheme makes the design process of the IT-2 fuzzy Formation Controller (FC) more straightforward and effective. According to the communication interaction protocol, the IT-2 Containment Controller (CC) design approach is proposed for followers to ensure convergence into the region defined by the leaders. Leveraging the IT-2 T-SFM representation, the analysis methods developed for linear Multi-Agent Systems (MASs) are successfully extended to perform containment analysis without requiring the additional assumptions imposed in existing research. Notably, the IT-2 fuzzy tracking controller can also be applied in collision avoidance situations to track the desired trajectories calculated by the avoidance algorithm under the Artificial Potential Field (APF). Benefiting from the combination of vortex and source APFs, the leaders can properly adjust the system dynamics to prevent potential collision risk. Integrating the fuzzy theory and APFs avoidance algorithm, an IT-2 fuzzy controller design approach is proposed to achieve the F-and-C purpose while ensuring collision avoidance capability. Finally, a multi-ship simulation is conducted to validate the feasibility and effectiveness of the designed IT-2 fuzzy controller.