Solving the Formation and Containment Control Problem of Nonlinear Multi-Boiler Systems Based on Interval Type-2 Takagi–Sugeno Fuzzy Models

Abstract

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.

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“…The ANFIS, originating in the early 1990s, is a specialized form of an artificial neural network [35]. It combines the interpretability of fuzzy systems with the learning capabilities of neural networks, specifically based on the Takagi-Sugeno fuzzy inference system [36]. The fundamental principle of ANFIS revolves around mapping inputs to outputs through a sequence of fuzzy IF-THEN rules and learning algorithms.…”